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Algebraic aspects of increasing subsequences

Jinho Baik·Eric M. Rains
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Abstract

We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points; new formulae for partial Cauchy-Littlewood sums, as well as new proofs of old formulae; relations of these expressions to orthogonal polynomials on the unit circle; and explicit bases for invariant spaces of the classical groups, together with appropriate generalizations of the straightening algorithm.

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Jinho Baik, Eric M. Rains. 2000-09-26. Algebraic aspects of increasing subsequences. https://arxiv.org/abs/math/9905083

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