2016/10/31 by Alejandro H. Morales, Igor Pak, Greta Panova · 1 citation
Mathematics · #math.CO #msc:05A05 #msc:05A15 #msc:05A19 #msc:05E05
paper · pdf · doi:10.1137/16m1099625
published as SIAM Journal of Discrete Math., 31 (2017), 1953--1989 · 33 pages, 10 figures. This is the second paper of the series "Hook formulas for skew shapes". Most of Sections 8 and 9 in this paper used to be part of arxiv:1512.08348 (v1,v2); v2 fixed several typos; v3 made precision in definition of flagged tableaux in Section 3.2 and fixed typo in Example 3.3; v4 fixed small typos in proof of Corollary 7.6
arxiv created 2020/06/02 · arxiv updated 2020/06/03
The Naruse hook-length formula is a recent general formula for the number of standard Young tableaux of skew shapes, given as a positive sum over excited diagrams of products of hook-lengths. In 2015 we gave two different q-analogues of Naruse's formula: for the skew Schur functions, and for counting reverse plane partitions of skew shapes. In this paper we give an elementary proof of Naruse's formula based on the case of border strips. For special border strips, we obtain curious new formulas for the Euler and q-Euler numbers in terms of certain Dyck path summations.