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October, 2021 Sign-balances of Tableaux with at Most Three Rows
Tung-Shan Fu, Chien-Tai Ting
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Taiwanese J. Math. 25(5): 867-885 (October, 2021). DOI: 10.11650/tjm/210305


Let the sign of a standard Young tableau (SYT) be the sign of the permutation obtained by reading the entries row by row from left to right, starting from the top row. By a sign-reversing involution on the tableaux in terms of lattice paths, we obtain the sign-balance of $n$-cell SYTs of all shapes with at most three rows. For skew shapes, we obtain partial results on the sign-balance enumeration of $2n$-cell skew SYTs of all shapes with at most three rows, under a parity condition of the skew part.

Funding Statement

The first author was supported in part by Ministry of Science and Technology (MOST) grant 109-2115-M-153-004-MY2.


The authors thank the referees for carefully reading the manuscript and providing helpful suggestions.


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Tung-Shan Fu. Chien-Tai Ting. "Sign-balances of Tableaux with at Most Three Rows." Taiwanese J. Math. 25 (5) 867 - 885, October, 2021.


Received: 5 February 2021; Revised: 14 March 2021; Accepted: 14 March 2021; Published: October, 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.11650/tjm/210305

Primary: 05A15
Secondary: 05A19

Rights: Copyright © 2021 The Mathematical Society of the Republic of China


Vol.25 • No. 5 • October, 2021
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