The Enumeration Formula of Standard Young Tableaux for Approximate Right Triangles
DOI:
https://doi.org/10.6919/ICJE.202506_11(6).0017Keywords:
Standard Young Tableaux; Hollow Shifted Shapes; Multiple Integral; Catalan Number.Abstract
The correspondence between nested order statistics and standard Young tableaux reveals a profound link between probability theory and combinatorics. By interpreting standard Young tableaux as nested order statistics constructions, the enumeration problem transforms into computing multiple integrals over simplex domains constrained by nested order statistics. This probabilistic-combinatorial duality enables analytical techniques from integral geometry to estimate standard Young tableaux counts. Otherwise, we combine with the combinatorial identity, the general summation representation of hollow shifted standard Young tableaux with approximately right-angled trapezoids is given, thus verifying the conjecture in the literature.
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