## Recent preprints

- Counting pattern-avoiding permutations by big descents (with Johnny Rivera Jr. and Y. Zhuang),
*preprint*, arXiv:2408.15111. - Penney's game for permutations (with Y. Lin),
*preprint*, arXiv:2404.06585. - Canon permutations and generalized descents of standard Young tableaux,
*preprint*, arXiv:2403.14914. - Triangular partitions: enumeration, structure, and generation (with A. Galván),
*preprint*, arXiv:2312.16353. Code available here. - Statistics on clusters and r-Stirling permutations (with J. Troyka and Y. Zhuang),
*preprint*, arXiv:2209.12436, to appear in*J. Comb.*

## Journal publications

- On individual leaf depths of trees,
*Discrete Appl. Math. 353 (2024), 151-180*. arXiv:2302.05252. - Descents on nonnesting multipermutations,
*European J. Combin. (2023)*. arXiv:2204.00165. - Rowmotion on 321-avoiding permutations (with B. Adenbaum),
*Electron. J. Combin. 30(3) (2023), #P3.5, 26 pp.*. arXiv:2212.11347. - Rowmotion on fences (with M. Plante, T. Roby and B. Sagan),
*Algebr. Comb. 6 (2023), no. 1, 17-36*. arXiv:2108.12443. - Partitions with constrained ranks and lattice paths (with S. Corteel and C. Savage),
*ECA 3:3 (2023) Article #S2R18*. arXiv:2211.08933. - On a dart game of Niedermaier,
*Adv. in Appl. Math. 145 (2023) 102483*. arXiv:2209.03775. - Counting lattice paths by crossings and major index II: tracking descents via two-rowed arrays,
*Sém. Lothar. Combin. 87B (2023), Art. #7, 36 pp.*arXiv:2112.05696. - Partial rank symmetry of distributive lattices for fences (with B. Sagan),
*Ann. Comb. 27 (2023), no. 2, 433-454*. arXiv:2201.03044. - Counting lattice paths by crossings and major index I: the corner-flipping bijections,
*Combinatorial Theory 2 (2) (2022), #14*. arXiv:2106.09878. - Cyclic pattern containment and avoidance (with R. Domagalski, J. Liang, Q. Minnich, B. Sagan, J. Schmidt and A. Sietsema),
*Adv. in Appl. Math. 135 (2022), 102320*. [Download] - The degree of asymmetry of sequences (with E. Deutsch),
*ECA 2:1 (2022) Article S2R7*. arXiv:2107.06188. - The degree of symmetry of lattice paths,
*Ann. Comb. 25 (2021), 877-911*. arXiv:2002.12874. - Enumerating symmetric peaks in non-decreasing Dyck paths (with R. Florez and J.L. Ramirez),
*Ars Math. Contemp. 21 (2021) #P2.04*. - Bijections for restricted inversion sequences and permutations with fixed points,
*Australas. J. Combin. 80 (2021), 106-115*. arXiv:2006.13842. - Descents on quasi-Stirling permutations,
*J. Combin. Theory Ser. A, 180 (2021) 105429*. arXiv:2002.00985. - Symmetric peaks and symmetric valleys in Dyck paths,
*Discrete Math. 344 (2021), 112364*. arXiv:2008.05669. - Pervasive chromosomal instability and karyotype order during tumour evolution (with T. Watkins, E. Lim, M. Petkovic, ...,
R. Schwarz,
N. McGranahan,
C. Swanton),
*Nature 587, 126-132 (2020)*. - Wilf equivalences between vincular patterns in inversion sequences (with J.S. Auli),
*Appl. Math. Comput. 388 (2020) 125514*. arXiv:2003.11533. - A simple bijective proof of a familiar derangement recurrence,
*Fibonacci Quart. 59 (2021), 150--151*. arXiv:2005.11312. - On cyclic Schur-positive sets of permutations (with J. Bloom and Y. Roichman),
*Electron. J. Combin. 27(2) (2020), #P2.6*. arXiv:1908.07920. - Consecutive patterns in inversion sequences II: avoiding patterns of relations (with J.S. Auli),
*J. Integer Seq. 22 (2019), Art. 19.7.5*. arXiv:1906.07365. - Consecutive patterns in inversion sequences (with J.S. Auli),
*Discrete Math. Theor. Comput. Sci. 21:2 (2019), #6*. arXiv:1904.02694. - Characterizations and enumerations of patterns of signed shifts (with K. Moore),
*Discrete Appl. Math. 277 (2020), 92-114*. arXiv:1711.05213. - Exact and asymptotic enumeration of cyclic permutations according to descent set (with J. Troyka),
*J. Combin. Theory Ser. A 165 (2019), 360-391*. arXiv:1710.05103. - Cyclic descents for near-hook and two-row shapes (with R. Adin and Y. Roichman),
*European J. Combin. 79 (2019), 152-178*. arXiv:1801.00044. - A Markov chain for numerical chromosomal instability in clonally expanding populations (with A. Laughney and S. Bakhoum),
*PLoS Comput. Biol. 14(9): e1006447*. [Here is the submitted version that includes supplementary figures and end-of-proof marks.] - Wilf equivalence relations for consecutive patterns (with T. Dwyer),
*Adv. in Appl. Math. 99 (2018), 134-157*. arXiv:1801.08262. - A bijection between bargraphs and Dyck paths (with E. Deutsch),
*Discrete Appl. Math. 251 (2018), 340-344*. arXiv:1705.05984. - Continued fractions for permutation statistics,
*Discrete Math. Theor. Comput. Sci. 19 (2018), #11*. arXiv:1703.08742. - The probability of avoiding consecutive patterns in the Mallows distribution (with H. Crane and S. DeSalvo),
*Random Structures Algorithms 53 (2018), 417-447*. arXiv:1609.01370. - On rotated Schur-positive sets (with Y. Roichman),
*J. Combin. Theory Ser. A 152 (2017), 121-137*. arXiv:1609.07335. - Character formulas and descents for the hyperoctahedral group (with R. Adin, C. Athanasiadis and Y. Roichman),
*Adv. in Appl. Math. 87 (2017), 128-169*. arXiv:1504.01283. - The structure of the consecutive pattern poset (with
P. McNamara),
*Int. Math. Res. Not. IMRN 2018, no.7, 2099-2134*. arXiv:1508.05963. - Statistics on bargraphs viewed as cornerless Motzkin paths (with E. Deutsch),
*Discrete Appl. Math. 221 (2017), 54-66*. arXiv:1609.00088. - Two descent statistics over 321-avoiding centrosymmetric involutions
(with M. Barnabei,
F. Bonetti and
M. Silimbani),
*Electron. J. Combin. 23 (2016), #P1.35*. arXiv:1508.07515. - Schur-positive sets of permutations via products of grid classes (with Y. Roichman),
*J. Algebraic Combin. 45 (2017), 363-405*. arXiv:1509.00045. - Symmetries of statistics on lattice paths between two boundaries (with M. Rubey),
*Adv. Math. 287 (2016), 347-388*. arXiv:1305.2206. - Dynamics of tumor heterogeneity derived from clonal karyotypic evolution (with A. Laughney, S. Bakhoum and G. Genovese),
*Cell Rep. 12 (2015), 809-820*. - Bijections for pairs of non-crossing lattice paths and walks in the plane,
*European J. Combin. 49 (2015), 25-41*. arXiv:1406.1709. - Signed arc permutations (with Y. Roichman),
*J. Comb. 6 (2015), 205-234*. arXiv:1402.0211. - A generating tree approach to k-nonnesting partitions and permutations (with M. Mishna,
S. Burrill and L. Yen),
*Ann. Comb. 20 (2016), 453-485*. arXiv:1108.5615. - Descent sets on 321-avoiding involutions and hook decompositions of partitions
(with M. Barnabei,
F. Bonetti , and
M. Silimbani),
*J. Combin. Theory Ser. A 128 (2014), 132-148*. arXiv:1401.3011. - Cyclic permutations realized by signed shifts
(with K.
Archer),
*J. Comb. 5 (2014), 1-30*. arXiv:1304.7790. - Arc permutations (with Y. Roichman),
*J. Algebraic Combin. 39 (2014), 301-334*. arXiv:1210.6056. - Inversion polynomials for 321-avoiding permutations (with S.-E. Cheng,
A. Kasraoui and B. Sagan),
*Discrete Math. 313 (2013), 2552-2565*. arXiv:1112.6014 (addendum: arXiv:1305.3845). - Total occurrence statistics on restricted permutations (with A. Burstein),
*Pure Math. Appl. (PU.M.A.) 24 (2013), 103-123*. arXiv:1305.3177. - The most and the least avoided consecutive patterns,
*Proc. Lond. Math. Soc. 106 (2013), 957-979*. arXiv:1203.1636. - Pattern avoidance in matchings and partitions (with J. Bloom),
*Electron. J. Combin. 20 (2013), #P5*. arXiv:1211.3442. - Clusters, generating functions and asymptotics for consecutive patterns in permutations (with M. Noy),
*Adv. in Appl. Math. 49 (2012), 351-374*. arXiv:1210.6061. - Fixed points and excedances in restricted permutations,
*Electron. J. Combin. 18 (2012), #P29*. - Restricted simsun permutations (with E. Deutsch),
*Ann. Comb. 16 (2012), 253-269*. arXiv:0912.1361. - Permutations and β-shifts,
*J. Combin. Theory Ser. A 118 (2011), 2474-2497*. arXiv:1008.4167. - Descent sets of cyclic permutations,
*Adv. in Appl. Math. 47 (2011), 688-709*. arXiv:0906.2795. - On basic forbidden patterns of functions (with Y. Liu),
*Discrete Appl. Math 159 (2011), 1207-1216*. arXiv:0909.2277. - Cycle-up-down permutations (with E. Deutsch),
*Australas. J. Combin. 50 (2011), 187-199*. arXiv:0909.5199. - The X-class and almost-increasing permutations,
*Ann. Comb. 15 (2011), 51-68*. arXiv:0710.5168. - Improved bounds on the number of numerical semigroups of a given genus,
*J. Pure Appl. Algebra 214 (2010), 1862-1873*. arXiv:0905.0489. - The largest and the smallest fixed points of permutations (with E. Deutsch),
*European J. Combin. 31 (2010), 1404-1409*. arXiv:0904.2792. - The number of permutations realized by a shift,
*SIAM J. Discrete Math. 23 (2009), 765-786*. arXiv:0909.2274. - Forbidden patterns and shift systems (with
J.M. Amigó and M.B. Kennel),
*J. Combin. Theory Ser. A 115 (2008), 485-504*. arXiv:0707.4628. - Generating trees for permutations avoiding generalized patterns,
*Ann. Comb. 11 (2007), 435-458*. arXiv:0707.4633. - A bijection between 2-triangulations and pairs of non-crossing Dyck paths,
*J. Combin. Theory Ser. A 114/8 (2007), 1481-1503*. arXiv:math.CO/0610235. - Bounds on the number of inference functions of a graphical model (with K. Woods),
*Statist. Sinica 17 (2007), 1395-1415*. arXiv:math.CO/0610233. - The probability of choosing primitive sets (with K. Woods),
*J. Number Theory 125 (2007), 39-49*. arXiv:math.NT/0607390. - Restricted Dumont permutations, Dyck paths, and noncrossing partitions (with A. Burstein and T. Mansour),
*Discrete Math. 306 (2006), 2851-2869*. arXiv:math/0610234. - Combinatòria i biologia: funcions d'inferència i alineació de seqüències,
*Butl. Soc. Catalana Mat. 21 (2006), n. 1, 39-52*. [Download] - Asymptotic enumeration of permutations avoiding generalized patterns,
*Adv. in Appl. Math. 36 (2006), 138-155*. arXiv:math/0505254. - Old and young leaves on plane trees (with W.C. Chen and E. Deutsch),
*European J. Combin. 27 (2006), 414-427*. arXiv:math/0410127. - Restricted Motzkin permutations, Motzkin paths, continued fractions, and Chebyshev polynomials (with T. Mansour),
*Discrete Math. 305 (2005), 170-189*. arXiv:math/0610237. - Multiple pattern-avoidance with respect to fixed points and excedances,
*Electron. J. Combin. 11 (2004), #R51*. arXiv:math/0311211. - Bijections for refined restricted permutations (with I. Pak),
*J. Combin. Theory Ser. A 105 (2004), 207-219*. arXiv:math/0212328. - A simple and unusual bijection for Dyck paths and its consequences (with E. Deutsch),
*Ann. Comb. 7 (2003), 281-297*. arXiv:math/0306125. - Consecutive patterns in permutations (with M. Noy),
*Adv. in Appl. Math. 30 (2003), 110-125*. [Download]

## Book Chapters

- A survey of consecutive patterns in permutations, chapter of the book
*Recent Trends in Combinatorics (IMA Volume in Mathematics and its Applications) 601-618*, Springer, 2016. arXiv:1504.07265. - Inference functions, chapter of the book
*Algebraic Statistics for Computational Biology*, edited by L. Pachter and B. Sturmfels, Cambridge University Press, 2005. - Bounds for optimal sequence alignment (with F. Lam), chapter of the
book
*Algebraic Statistics for Computational Biology*, edited by L. Pachter and B. Sturmfels, Cambridge University Press, 2005.

## Refereed Conference Proceedings

- Combinatorial Properties of Triangular Partitions (with A. Galván),
*Proceedings of FPSAC 2024, Sém. Lothar. Combin. 91B.68 (2024), 12 pp*. - The Distribution of Descents on Nonnesting Permutations,
*Proceedings of FPSAC 2023, Sém. Lothar. Combin. 89B.2 (2023), 12 pp*. - Rowmotion on 321-Avoiding Permutations,
*Proceedings of FPSAC 2023, Sém. Lothar. Combin. 89B.16 (2023), 12 pp*. - Walks in Simplices, Cylindric Tableaux, and Asymmetric Exclusion Processes,
*Proceedings of FPSAC 2022, Sém. Lothar. Combin. 86B.8 (2022), 12 pp*. - Rowmotion on fences (with M. Plante, T. Roby and B. Sagan),
*Proceedings of FPSAC 2022, Sém. Lothar. Combin. 86B.40 (2022), 12 pp*. - Enumerating Descents on Quasi-Stirling Permutations and Plane Trees,
*Extended Abstracts EuroComb 2021, Trends in Mathematics, vol 14. Birkhäuser, Cham., pp 32-37*. - Measuring Symmetry in Lattice Paths and Partitions,
*Proceedings of FPSAC 2020, Sém. Lothar. Combin. 84B (2020), Article #26, 12 pp*. - Inversion Sequences Avoiding Consecutive Patterns (with J.S. Auli),
*Proceedings of FPSAC 2020, Sém. Lothar. Combin. 84B (2020), Article #27, 12 pp*. - The number of cycles with a given descent set (with J. Troyka),
*Proceedings of FPSAC 2018, Sém. Lothar. Combin. 80B (2018), Article #8, 12 pp*. - Cyclic descent extensions and distributions (with R. Adin, V. Reiner and Y. Roichman),
*Proceedings of the GASCom 2018 Workshop, 32--42*. - A necessary condition for c-Wilf equivalence (with T. Dwyer),
*Proceedings of FPSAC 2017, Sém. Lothar. Combin. 78B (2017), Article #69, 12 pp*. - Patterns of negative shifts and signed shifts (with K. Archer and K. Moore),
*Proceedings of FPSAC 2017, Sém. Lothar. Combin. 78B (2017), Article #49, 12 pp*. - Schur-positivity via products of grid classes (with Y. Roichman),
*Proceedings of FPSAC 2016, Discrete Math. Theor. Comput. Sci. proc. BC (2016), 443--454*. - On intervals of the consecutive pattern poset (with P. McNamara),
*Proceedings of FPSAC 2016, Discrete Math. Theor. Comput. Sci. proc. BC (2016), 431--442*. - The frequency of pattern occurrence in random walks (with M. Martinez),
*Proceedings of FPSAC 2015, Discrete Math. Theor. Comput. Sci. proc. FPSAC'15 (2015), 217-228*. - Periodic patterns of signed shifts (with K. Archer),
*Proceedings of FPSAC 2013, Discrete Math. Theor. Comput. Sci. proc. AS (2013), 873-884*. - Patterns in matchings and rook placements (with J. Bloom),
*Proceedings of FPSAC 2013, Discrete Math. Theor. Comput. Sci. proc. AS (2013), 909-920*. - Bijections for lattice paths between two boundaries (with M. Rubey),
*Proceedings of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR (2012), 827-838*. - Arc Permutations (extended abstract) (with Y. Roichman),
*Proceedings of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR (2012), 259-270*. - Consecutive patterns in permutations: clusters and generating functions (with M. Noy),
*Proceedings of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR (2012), 247-258*. - Generating trees for partitions and permutations with no k-nestings (with M. Mishna,
S. Burrill and L. Yen),
*Proceedings of FPSAC 2012, Discrete Math. Theor. Comput. Sci. proc. AR (2012), 409-420*. - Allowed patterns of beta-shifts,
*Proceedings of FPSAC 2011, Discrete Math. Theor. Comput. Sci. proc. AO (2011), 293-304*. - Sorting by Placement and Shift (with P. Winkler),
*Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009*. arXiv:0809.2957. - Permutations realized by shifts,
*Proceedings of FPSAC 2009, Discrete Math. Theor. Comput. Sci. proc. AK (2009), 361-372*. - Pattern avoidance in dynamical systems (with J.M. Amigó and M.B. Kennel),
*Proceedings of FPSAC 2008, Discrete Math. Theor. Comput. Sci. proc. AJ (2008), 71-82*. - A bijection between 2-triangulations and pairs of non-crossing Dyck paths,
*Proceedings of FPSAC 2007*. - Bounds on the number of inference functions of a graphical model (with K. Woods),
*Proceedings of FPSAC 2006*. - Old and young leaves on plane and binary trees (with E. Deutsch),
*Proceedings of FPSAC 2005*. - Restricted Motzkin permutations (with T. Mansour),
*Proceedings of FPSAC 2004*. - Fixed points and excedances in restricted permutations,
*Proceedings of FPSAC 2003*. arxiv:math.CO/0212221. - Forbidden subwords in permutations (with M. Noy),
*Proceedings of FPSAC 2001*.

## Slides and videos of selected presentations

- Combinatorial properties of triangular partitions, [Michigan Tech University, Seminar in Partition Theory, q-Series and Related Topics, January 2024]. Video recording.
- Descents on noncrossing and nonnesting permutations, [Queen Mary, University of London, February 2023]. Here is the video recording of a similar talk at the NY Combinatorics Seminar.
- Counting lattice paths by the number of crossings, major index, and descents, [Combinatorial and Algebraic Enumeration, Waterloo, Canada, May 2022].
- Partial rank symmetry of distributive lattices for fences, [University of Minnesota Combinatorics Seminar, April 2022].
- Rowmotion on 321-avoiding permutations, [BIRS Dynamical Algebraic Combinatorics workshop, November 2021]. Here is the video recording of the talk.
- Counting lattice paths by the number of crossings and major index, [Lattice Paths, Combinatorics and Interactions, June 2021].
- Bijections for derangements and pattern-avoiding inversion sequences, [Permutation Patterns 2021 Virtual Workshop, June 2021].
- Descents on quasi-Stirling permutations, [UMass Amherst Discrete Math Seminar, March 2020], [UVM Combinatorics Seminar, September 2021].
- The probability of avoiding consecutive patterns in the Mallows distribution, [Joint Mathematics Meetings, Denver, CO, January 2020].
- Consecutive patterns in permutations and inversion sequences, [Virtual Combinatorics Colloquium, December 2019]. Here is the video of my virtual talk. Check out the VCC webpage.
- Consecutive patterns in inversion sequences, [AMS Fall Southeastern Sectional Meeting, Gainesville, FL, November 2019].
- A Markov-chain model of chromosomal instability, [Dagstuhl Seminar on Genomics, Pattern Avoidance, and Statistical Mechanics, November 2018].
- Schur-positive grid classes and cyclic descents of SYT, [Oberwolfach Research Institute for Mathematics (MFO), Workshop on Enumerative Combinatorics, May 2018].
- Cyclic descents of standard Young tableaux, [Workshop on Algorithmic and Enumerative Combinatorics, ESI, Vienna, October 2017].
- The structure of the consecutive pattern poset, [MIT Combinatorics Seminar, March 2017].
- Schur-positive grid classes, [Keynote talk, Graduate Student Combinatorics Conference, Clemson University, April 2016].
- A Markov chain to probe chromosomal instability in tumor evolution and drug resistance [Sloan-Kettering Institute, Computational Biology Program, August 2015].
- Some unsolved problems in mathematics and computation [Johns Hopkins Center for Talented Youth, October 2014].
- Two EC tidbits [Richard Stanley's 70th Birthday Conference, June 2014].
- Consecutive patterns in permutations [Plenary talk at Permutation Patterns 2013; Video of talk at IMA, November 2014].
- Bijections for lattice paths between two boundaries [SIAM DM'12, CanaDAM 2013].
- Consecutive patterns in permutations: clusters, generating functions, and asymptotics [Slides February 2012].
- Allowed patterns of β-shifts [FPSAC 2011 Slides]. Permutations and β-shifts [Slides October 2010].
- The number of numerical semigroups of a given genus [Slides June 2010]/
- Descent sets of cyclic permutations [Slides Oct 2009, Slides April 2010].
- Sorting by placement and shift [Slides Jan 2009]. A greedy sorting algorithm [Slides February 2010].
- Discrete
Mathematics Day, Middlebury College, September 2007,
*Forbidden patterns in telling random from deterministic time series*. [Slides] - MIT Combinatorics Seminar,
September 2006,
*A bijection between 2-triangulations and pairs of non-crossing Dyck paths.*[Slides] - International
Conference on Permutation Patterns, PP'06, Reykjavik, Iceland, June
2006,
*Generating trees for permutations avoiding generalized patterns.*[Slides] - Institut Mittag-Leffler
Seminar, Djursholm, Sweden, May 2005,
*Combinatorics from biology: inference functions and sequence alignment*. [Slides] - International
Conference on Permutation Patterns, PP'05, Gainesville, Florida, March
2005,
*Asymptotic enumeration of permutations avoiding generalized patterns.*[Slides] - MIT Combinatorics Seminar,
February 2005.
*Inference functions and sequence alignment.*[Slides] - Stanford
University Representation Theory Seminar, December 2004,
*Refined enumeration of pattern-avoiding permutations.*[Slides] - International Conference on Permutation
Patterns, PP'04, Nanaimo, Canada, July 2004,
*Simultaneous pattern-avoidance with respect to fixed points and excedances.*[Slides] - Thesis defense, MIT, April 2004,
*Statistics on Pattern-avoiding Permutations*. [Slides] - UC Berkeley
Combinatorics Seminar, February 2004,
*Refined enumeration of pattern-avoiding permutations*. [Slides] - MIT Combinatorics Seminar,
November 2003.
*Pattern-avoiding permutations: old results and new developments.*[Slides] - FPSAC 2003, Vadstena,
Sweden, June 2003.
*Fixed points and excedances in restricted permutations*. [Slides] - MIT Simple Person's Applied
Math Seminar, November 2002.
*What pattern avoidance shouldn't have avoided*. [Slides]

## Unpublished material

- Consecutive patterns in circular permutations (with B. Sagan), arXiv:2107.04717. (These results have been merged into paper 64 above.)
- An involution on lattice paths between two boundaries. [Download] (A version of this note appears as part of paper 37 above.)
- Statistics on Pattern-avoiding Permutations, Ph.D. thesis, MIT, 2004. [Download pdf, ps]