Abstract
In this paper the number of standard Young tableaux (SYT) is evaluated by the methods of multiple integrals and combinatorial summations. We obtain the product formulas of the numbers of skew SYT of certain truncated shapes, including the skew SYT $((n+k)^{r+1},n^{m-1}) / (n-1)^r $ truncated by a rectangle or nearly a rectangle, the skew SYT of truncated shape $((n+1)^3,n^{m-2}) / (n-2) \backslash \; (2^2)$, and the SYT of truncated shape $((n+1)^2,n^{m-2}) \backslash \; (2)$.
Highlights
The enumeration of standard Young tableaux (SYT) is a fundamental problem in enumerative combinatorics
The number of SYT is given by the well-known hook-length formulas [5]
Hook-length formulas cannot give the number of SYTs of truncated shapes
Summary
The enumeration of standard Young tableaux (SYT) is a fundamental problem in enumerative combinatorics. The number of SYT-type chart will be interpreted as distribution of nested order statistics in this paper. J=1 corresponds to a filling of the SYT-type chart of shape λ, the property of independent and identically distributed makes sure that all the outcomes of event A are likely. Based on this discrete structure, there is. Consider three groups of independent order statistics (ξ1,2, ξ2,2), (η1,2, η2,2),(τ1,3, τ2,3, τ3,3) from uniform distribution on (0, 1), the number of the SYT-type chart of shape (42, 3)/(12)\(1, 3) ∪ (2, 2) is given by ξ1,2 ξ2,2. The equivalent form of Selberg integral used in this paper is k (tj − ti)2γdt1 · · · dtk 0
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