Department of

September 2018October 2018November 2018 Su Mo Tu We Th Fr Sa Su MoTuWe Th Fr Sa Su Mo Tu We Th Fr Sa 1 1 2 3 4 5 6 1 2 3 2 3 4 5 6 7 8 7 8 9 10 11 12 13 4 5 6 7 8 9 10 9 10 11 12 13 14 15 14 151617 18 19 20 11 12 13 14 15 16 17 16 17 18 19 20 21 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24 23 24 25 26 27 28 29 28 29 30 31 25 26 27 28 29 30 30

Thursday, February 1, 2018

**Abstract:** Edelman and Greene constructed a bijection between the set of standard Young tableaux and the set of balanced Young tableaux of the same shape. Fomin, Greene, Reiner and Shimozono introduced the notion of balanced Rothe tableaux of a permutation w, and established a bijection between the set of balanced Rothe tableaux of w and the set of reduced words of w. In this talk, we introduce the notion of standard Rothe tableaux of w, which are tableaux obtained by labelling the cells of the Rothe diagram of w such that each row and each column is increasing. We show that the number of standard Rothe tableaux of w is smaller than or equal to the number of balanced Rothe tableaux of w, with equality if and only if w avoids the four patterns 2413, 2431, 3142 and 4132. When w is a dominant permutation, i.e., 132-avoiding, the Rothe diagram of w is a Young diagram, so our result generalizes the result of Edelman and Greene.

Thursday, February 8, 2018

Wednesday, February 21, 2018

Thursday, March 1, 2018

Thursday, March 8, 2018

Monday, April 2, 2018

Tuesday, April 3, 2018

Wednesday, April 4, 2018

Thursday, April 26, 2018

Thursday, May 3, 2018

Tuesday, May 29, 2018

Thursday, October 11, 2018

Thursday, November 29, 2018