Baik, Jinho; Rains, Eric M. Algebraic aspects of increasing subsequences. (English) Zbl 1007.05096 Duke Math. J. 109, No. 1, 1-65 (2001). Summary: 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. Cited in 3 ReviewsCited in 81 Documents MSC: 05E15 Combinatorial aspects of groups and algebras (MSC2010) 05A15 Exact enumeration problems, generating functions 05E05 Symmetric functions and generalizations 60C05 Combinatorial probability 05E35 Orthogonal polynomials (combinatorics) (MSC2000) Keywords:partial Cauchy-Littlewood sums; subsequences of permutations; orthogonal polynomials; straightening algorithm PDFBibTeX XMLCite \textit{J. Baik} and \textit{E. M. Rains}, Duke Math. J. 109, No. 1, 1--65 (2001; Zbl 1007.05096) Full Text: DOI arXiv Euclid