Generalizations of Cauchy’s summation theorem for Schur functions. (English) Zbl 0707.05061
Summary: Cauchy’s summation theorem for Schur functions is generalized, and a number of related results are given. The result is applied to a combinatorial problem involving products of pairs of permutations, by appeal to properties of the group algebra of the symmetric group.
MSC:
| 05E05 | Symmetric functions and generalizations |
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
| 05A15 | Exact enumeration problems, generating functions |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
