On the sign-imbalance of skew partition shapes

Authors:
Jonas Sjöstrand
Affiliations:
Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Venue:
European Journal of Combinatorics
Year:
2007

Citing 6
Cited 2

Enumerative combinatorics

Enumerative combinatorics
Robinson-Schensted algorithms for Skew tableaux

Journal of Combinatorial Theory Series A
Generating linear extensions of posets by transpositions

Journal of Combinatorial Theory Series B
Sign-balanced posets

Journal of Combinatorial Theory Series A
Growth diagrams, domino insertion and sign-imbalance

Journal of Combinatorial Theory Series A
On the sign-imbalance of partition shapes

Journal of Combinatorial Theory Series A

Signed differential posets and sign-imbalance

Journal of Combinatorial Theory Series A
Skew domino Schensted correspondence and sign-imbalance

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan and Stanley. The result is a remarkably simple generalization of the ordinary non-skew formula. The sum of the signs of all standard tableaux on a given skew shape is the sign-imbalance of that shape. We generalize previous results on the sign-imbalance of ordinary partition shapes to skew ones.