Professor of Mathematics

"My work has always tried to unite the true with the beautiful and when I had to choose one or the other, I usually chose the beautiful." -- Hermann Weyl.

Research supported in part by the National Science Foundation |

The lattice of submonoids of the
uniform block permutations containing the symmetric group

(with F. Saliola, A. Schilling, and M. Zabrocki)
preprint (2024).

The chromatic symmetric function in the star-basis (with M. Gonzalez and M. Tomba) preprint (2024).

From quasi-symmetric to Schur expansions with applications to
symmetric chain decompositions and plethysm

(with F. Saliola, A. Schilling and M. Zabrocki)
preprint (2024).

The mystery of plethysm coefficients
(with L. Colmenarejo, F. Saliola, A. Schilling and M. Zabrocki)

Proceedings of Symposia in Pure Mathematics, to appear (2024).

Representations of quasi-partition algebras (with N. Wallace and M. Zabrocki), to appear in Journal of Algebra (2024).

The symmetric group through a dual perspective (with M. Zabrocki) Notices Amer. Math. Soc. 70 (2023),

no. 6, 897–904.

Marked Graphs and the Chromatic
Symmetric Function (with J. Aliste-Prieto, A. De Mier and J. Zamora)

SIAM J. Discrete Math. 37 (2023), no. 3, 1881–1919.

Howe duality of the symmetric group
and a multiset partition algebra (with M. Zabrocki)

51 (2023), no. 1, 393–413.

Plethysm and the algebra of
uniform block permutations (with F. Saliola, A. Schilling and M. Zabrocki)

Symmetric group characters as symmetric functions
(with M. Zabrocki)

Paper No. 107943, 34 pp.

The Hopf structure of symmetric group
characters as symmetric functions (with M. Zabrocki)

A combinatorial model for the
decomposition of multivariate polynomials rings as an $S_n$-module

(with M. Zabrocki) *The Elect. Journal of Comb.*
**27(3)** (2020), #P3.24.

An insertion algorithm on multiset
partitions with applications to diagram algebras (with L. Colmenarejo,

F. Saliola, A. Schilling and M. Zabrocki)
*Journal of Algebra*, ** 557** (2020), 97128.

Commutation and normal ordering for operators on symmetric functions
(with E. Briand, P. McNamara

and M. Rosas), *Sém. Lothar. Combin.* **80** (2019), Article B80d.

Products of characters of the symmetric group
(with M. Zabrocki) *Journal of Combinatorial Theory, Series A,*

165, (2019), pages 299-324.

A minimaj-preserving crystal on ordered multiset partitions
(with G. Benkart, L. Colmenarejo, P. Harris,

G. Panova, A. Schilling, and M. Yip), *Advances in Applied Math.* Volume 95, April 2018, Pages 96–115.

The number of permutations with the same peak set for sign permutations (with F. Castro-Velez, A. Diaz-

Lopez, J. Pastrana and R. Zevallos), *Journal of Combinatorics,* Vol. ** 8 **, No. 4 (2017), pp. 631-652.

Rectangular symmetries for coefficients of symmetric functions (with E. Briand and M. Rosas),

*Elect. Journal of Comb.*, vol. **22, (3)**, (2015), #P3-15.

The partition algebra and the Kronecker coefficients (with C. Bowman and M. De Visscher),

*Trans. Amer. Math. Soc.* **367** (2015), no. 5, 3647–3667.

Schur positivity in a square (with C. Ballantine),
*The Elect. Journal of Comb.* **21 (3)** (2014), #P3.46

Graphs with equal chromatic
symmetric function (with G. Scott), *Discrete Mathematics*, Volume **320**,

6 April 2014, Pages 1-14

The quasi-partition algebra (with Z. Daugherty),
*Journal of Algebra*, Volume **404**, 15 February 2014,

Pages 124-151.

The partition algebra and the Kronecker product (with C. Bowman and M. De Visscher),
*Discrete Math. Theor. Comput. Sci. proc. *AS 2013, 321 - 332.

The stability of the Kronecker product of Schur functions (with E. Briand and M. Rosas),
*Discrete Math. Theor. Comput. Sci. Proc.*, AN, pp. 557-567, Nancy, 2010.

The stability of the Kronecker product of Schur functions (with E. Briand and M. Rosas)
*J. Algebra*

**331** (2011), 11-27.

Quasipolynomial formulas for the
Kronecker coefficients indexed by two two-row shapes (with E.

Briand and M. Rosas), FPSAC 2009, Hagenberg, Austria, *Discrete Mathematics and Theoretical
Computer Science Proc.* AK, 2009, 241-252

Reduced Kronecker coefficients and counter-examples to Mulmuley's saturation conjecture SH, with an

appendix by Ketan Mulmuley (with E. Briand and M. Rosas),
*Computational Complexity* **18** (2009),

no. 4, 577-600

The Hilbert series for the ring of Hook Schur functions (with M. Zabrocki), Preprint.

Cyclotomic Solomon Algebras (with A. Mathas),
Adv. Math. **219** (2008), no. 2, 450--487.

The Hopf Algebra of Uniform block Permutations (with M. Aguiar),
* J. Algebraic Combin.* **28**

(2008), no. 1, 115--138.

An extended abstract of 13 pages appeared in:
Proceedings of the Formal Power Series and Algebraic

Combinatorics 2005 Available at:
http://lanl.arxiv.org/abs/math.RA/0505199.

On the partition algebras of complex reflection groups, *Journal of Algebra,*
**313** (2007) 590-616.

A combinatorial interpretation for the
coefficients in the Kronecker product s_{(n,n-p)}* s_\lambda

(with C. Ballantine), *Sém. Lothar. Combin. 54A (2006), Art. B54Af, 29 pp.*

Affine Braids, Markov traces and the category O,
(with A. Ram) Algebraic groups and homogeneous

spaces, 423-473,* Tata Inst. Fund. Res. Stud. Math., Tata Inst. Fund. Res., Mumbai, 2007.*

New Results on the Peak algebra (with M. Aguiar and K. Nyman), J. of
Algebraic Combinatorics.

Vol. **23**, No.2 (2006), pg. 149-188

On the Kronecker product $s_{(n-p,p)}\ast s_{\lambda}$
(with C. Ballantine), Elec. Journal of

Combinatorics. Vol. **12**, (2005), #R28, 1-26.

On the algebraic decomposition of centralizer algebras of the hyperoctahedral group,
Contemporary

Math. 376, (2005), 345-357.

Rooted trees and the representation theory of iterated wreath products of abelian groups (with M.

Orrison and D. Rockmore), Adv. in Applied Math. **33**, Issue 3, (2004),
531-547.

q-Centralizer algebras for spin groups (with H. Wenzl),
Journal of Algebra, **253** (2002) 237-275.

Hecke algebras of type B and type D and Subfactors,
Pacific Journal of Math. Vol **199**, No. 1 (2001)

137-161.

Markov traces and Hecke algebras at roots of unity,
Proceedings of the Formal Power
Series and Algebraic

Combinatorics, 1999. pp. 405-416.

Weights of Markov traces on Hecke algebras,
J. Reine Angew Math. **508**, (1999) 157-178.

The Hecke algebra of type B at roots of unity, Markov traces and subfactors. Ph.D. Thesis, UCSD 1999.