Algebraic aspects of increasing subsequences

Details Algebraic aspects of increasing subsequences Algebraic aspects of increasing subsequences

1999-05-13

arxiv.org/abs/math/9905083v3

Mathematics

Combinatorics

LaTeX+amsmath+eepic; 52 pages. Expanded introduction, new references, other minor changes

Scientific paper

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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