Department of

December 2017 January 2018 February 2018 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 1 2 3 4 5 6 1 2 3 3 4 5 6 7 8 9 7 8 9 10 11 12 13 4 5 6 7 8 9 10 10 11 12 13 14 15 16 14 15 16 17 18 19 20 11 12 13 14 15 16 17 17 18 19 20 21 22 23 21 22 23 24 25 26 27 18 19 20 21 22 23 24 24 25 26 27 28 29 30 28 29 30 31 25 26 27 28 31

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