Research PaperNo Access

A maxdrop statistic for standard Young tableaux

Mark Dukes

https://orcid.org/0000-0002-2779-2680

School of Mathematics and Statistics, University College Dublin, Ireland

E-mail Address: [email protected]

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and

Toufik Mansour

Department of Mathematics, University of Haifa, Israel

E-mail Address: [email protected]

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https://doi.org/10.1142/S1793830921501056Cited by:0 (Source: Crossref)

Abstract

In this paper, we introduce a new statistic on standard Young tableaux that is closely related to the maxdrop permutation statistic that was introduced by the first author. We prove that the value of the statistic must be attained at one of the corners of the standard Young tableau. We determine the coefficients of the generating function of this statistic over two-row standard Young tableaux having $n$ cells. We prove several results for this new statistic that include unimodality of the coefficients for the two-row case.

Keywords:

AMSC: 05A05, 05A15

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