## Introduction to Combinatorics

 General Information Syllabus Homework Assignments Exam Related

Homework assignments

Practice problems are not to be submitted, but are very important. We will discuss these in class. You are encouraged to make up similar problems for your own benefit. Please be sure that you understand these problems thoroughly.

Written assignments will be submitted in class. These will emphasize proofs, and must conform to the following proof-writing standards.

Extra credit problems are optional. They should be submitted with and treated like written assignments.

Week of Mar 7 -- Mar 9, 2005

 Wednesday, March 9: Read 4.3.4-4.3.5. Practice problems  (for next class period) 222-224. Written assignment  (due at end of class, March 9) TBA.
 Tuesday, March 8: Read 4.3.2-4.3.4. Practice problems  (for next class period) 213-221. Written assignment  (for Wednesday, March 9) 214, 215.

Week of Feb 28 -- Mar 4, 2005

 Friday, March 4: Read 4.2-4.3.1. Practice problems  (for next class period) 210-212. Written assignment  (for Wednesday, March 9) 210ce, 211. Extra credit  (for Wednesday, March 9) 210h. Compute rows 0-5 of the q-Pascal triangle (ending with the q-analogs of the 1 5 10 10 5 1 row of the regular triangle). Note that the q-analog of (4 choose 2) and the q-analog of 6 are different. Let x and y be noncommuting variables which satisfy yx = qxy. (Think of q as an alphabetizing fee for placing x and y in the correct order.) Find a formula for expressing (x + y)n as a sum of monomials of the form xkyn-k and prove it using induction.
 Wednesday, March 2: Read 4.2. Practice problems  (for next class period) 200-208. Written assignment  (for Wednesday, March 9) 200, 201, 203, 207, 208.
 Monday, February 28: Read 4.1.5-4.1.6. Practice problems  (for next class period) 192-199. Written assignment  (for Friday, March 4) 193, 194, 195. Extra credit  (for Friday, March 4) 199.

Week of Feb 21 -- Feb 25, 2005

 Friday, February 25: Read 4.1.3-4.1.4. Practice problems  (for next class period) 183-191. Written assignment  (for Friday, March 4) 183, 184, 189, 190, 191.
 Wednesday, February 23: Read 4.1-4.1.2. Practice problems  (for next class period) 176-182. Written assignment  (for Friday, February 25) 179, 181.

Week of Feb 14 -- Feb 18, 2005

 Friday, February 18: Read 3.3.4 - 3.3.5. Practice problems  (for next class period) 172 - 177. Written assignment  (for Friday, February 25) 173, 174, 176. Extra credit  (for Friday, February 25) 177. Draw the 4th partition lattice.
 Wednesday, February 16: Read 3.3.3. Practice problems  (for next class period) 168 - 171. Written assignment  (for Friday, February 18) 170, 171. Extra credit  (for Friday, February 25) 169.
 Monday, February 14: Read 3.1 - 3.3.3. Practice problems  (for next class period) 157 - 167. Written assignment  (for Friday, February 18) 161, 164, 165, 167.

Week of Feb 7 -- Feb 11, 2005

 Wednesday, February 9: Read 3.2.2 - 3.2.3. Practice problems  (for next class period) 143 - 152. Written assignment  (for Friday, February 18) 143, 145, 148, 151, 152. Extra credit  (for Friday, February 18) 153 - 156.
 Tuesday, February 8: Read 3.2.1. Practice problems  (for next class period) 134-140 Summarize   after 135. Written assignment  (for Friday, February 18) 134, 139. Extra credit  (for Friday, February 18) 141, 142.

Week of Jan 31 -- Feb 4, 2005

 Friday, February 4: Read 3.1.3 Practice problems  (for next class period) 124-132. Summarize   after 127. Discuss   Middle column of row 7 of 20-fold way. Written assignment  (for Wednesday, February 9) 125, 126, 131, 132.
 Wednesday, February 4: Read 3.1- 3.1.2. Practice problems  (for next class period) 122, 123. Discuss   Row 10, middle column of rows 5-6 of 20-fold way. Written assignment  (for Friday, February 4) 122, 123.
 Monday, January 31: Read 2.3.4 Practice problems  (for next class period) 117. Supplementary problems 2.4: 2-5, 9. Written assignment  (for Friday, February 4) Supplemenatry problem 2.4: 5.

Week of Jan 24 -- Jan 28, 2005

 Friday, January 28: Read 2.3.3 - 2.3.4. Practice problems  (for next class period) 109, 110, 113, 114. Summarize   after 116. Written assignment  (for Friday, February 4) 108, 111, 112, 115, 116.
 Wednesday, January 26: Read 2.2.3 - 2.3.2. Practice problems  (for next class period) 97, 100, 101, 104, 105, 106, 107. Summarize   after 97. Written assignment  (for Friday, January 28) 98, 99. Written assignment  (for Friday, February 4) 102, 103. Extra credit  (for Friday, January 28) 94, 96,
 Monday, January 24: Read 2.1-2.1.3, 2.2-2.2.1. Practice problems  (for next class period) 74, 75, 78, 87, 88, 89, 90. Summarize   after 92. Written assignment  (for Friday, January 28) 72, 73, 77, 91, 92.

Week of Jan 18 -- Jan 21, 2005

 Friday, January 21: Read Total nonnegativity handout.
 Wednesday, January 19: Read 1.3.2-1.3.3. Practice problems  (for next class period) 56, 58, 61, 63, 64, 66. Summarize   after 66. Written assignment  (for Friday, January 21) 57, 59. Written assignment  (for Friday, January 28) 62, 65. Extra credit  (for Friday, January 28) Supplementary problems: 5, 9, 12.
 Tuesday, January 18: Read 1.3.1-1.3.2. Practice problems  (for next class period) Compute the first few Catalan numbers (up to n = 6). Problem 6.19 from handout: parts r, o, b, vv. (Assume h, i.) 53, 55. Written assignment  (for Friday, January 21) Problem 6.19 from handout: parts e, n, hhh. (Assume h, i, r, o, b, vv.) 54. Extra credit  (for Friday, January 21) Any additional parts of Problem 6.19.

Week of Jan 10 -- Jan 14, 2005

 Friday, January 14: Read 1.2.6-1.3.1. Practice problems  (for next class period) 1.2.6-1.3.1: 42, 44, 45, 48, 49. Summarize   after 46. Written assignment  (for Friday, January 21) 1.2.6-1.3.1: 43, 46, 47, 50, 51abc Extra credit  (for Friday, January 21) 1.2.6-1.3.1: 52abcdf (assume 52e), 52e.
 Wednesday, January 12: Read 1.2.5-1.2.6. Practice problems  (for next class period) 1.2.5-1.2.6: 32, 33, 34, 36, 38. Written assignment  (for Friday, January 21) 1.2.5-1.2.6: 35, 37, 39, 41. Extra credit  (for Friday, January 21) 1.2.5-1.2.6: 40.
 Monday, January 10: Read 1.2.2-1.2.5. Practice problems  (for next class period) 1.2.2-1.2.5: 23, 24, 27, 31. Summarize   after 31. Written assignment  (for Friday, January 14) 1.2.2-1.2.5: 25, 26, 28, 30. Extra credit  (for Friday, January 14) 1.2.2-1.2.5: 29.

Week of Jan 4 -- Jan 7, 2005

 Friday, January 7: Read 1.2.1. Practice problems  (for next class period) 1.2.1: 12, 13, 14, 18. Written assignment  (for Friday, January 14) 1.2.1: 11, 15, 16, 20, 21. Extra credit  (for Friday, January 14) 1.2.1: 17, 19, 22.
 Wednesday, January 5: Read 1.1, 1.2. Practice problems  (for next class period) 1.2: 1, 3, 5, 6, 8. Written assignment  (for Friday, January 14) 1.2: 2, 7, 9, 10. Extra credit  (for Friday, January 14) 1.2: 4.