Standard Young tableaux and lattice paths
Shaun V. Ault
TL;DR
This paper uses lattice path counting to derive known and new formulas for counting standard Young tableaux, including a novel formula for tableaux of height at most three.
Contribution
It reproduces a classical formula via lattice paths and introduces a new formula for tableaux of height ≤ 3 using Fourier methods.
Findings
Reproduces the classical Young tableaux counting formula.
Derives a new formula for tableaux of height ≤ 3.
Employs Fourier methods of Ault and Kicey.
Abstract
Using lattice path counting arguments, we reproduce a well known formula for the number of standard Young tableaux. We also produce an interesting new formula for tableaux of height using the Fourier methods of Ault and Kicey.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Random Matrices and Applications