Counting Descents in Standard Young Tableaux
Ilia Barahovski
TL;DR
This paper investigates the distribution of descent numbers in standard Young tableaux, providing explicit formulas for two-row shapes and recursive solutions for three-row shapes with specific configurations.
Contribution
It introduces explicit formulas for counting tableaux with descents in two-row shapes and recursive methods for more complex three-row shapes.
Findings
Explicit formula for two-row tableaux with a given number of descents
Recursive formulas for three-row tableaux with one cell in the third row
Solutions for specific cases of three-row shapes
Abstract
This paper deals with the distribution of descent number in standard Young tableaux of certain shapes. A simple explicit formula is presented for the number of tableaux of any shape with two rows, with any specified number of descents. For shapes of three rows with one cell in the third row recursive formulas are given, and are solved in certain cases.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Random Matrices and Applications