Determinant Formulas Relating to Tableaux of Bounded Height

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dc.creatorXin, Guoce
dc.date2007-04-25
dc.date.accessioned2026-07-07T07:58:13Z
dc.date.available2026-07-07T07:58:13Z
dc.descriptionChen et al. recently established bijections for $(d+1)$-noncrossing/ nonnesting matchings, oscillating tableaux of bounded height $d$, and oscillating lattice walks in the $d$-dimensional Weyl chamber. Stanley asked what is the total number of such tableaux of length $n$ and of any shape. We find a determinant formula for the exponential generating function. The same idea applies to prove Gessel's remarkable determinant formula for permutations with bounded length of increasing subsequences. We also give short algebraic derivations for some results of the reflection principle.
dc.description15 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0704.3381
dc.identifierhttp://arxiv.org/abs/0704.3381
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127926
dc.subjectCombinatorics
dc.subjectCommutative Algebra
dc.subject05A15; 05A18, 05E10
dc.titleDeterminant Formulas Relating to Tableaux of Bounded Height
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