Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: MSC category 15A15 ( Determinants, permanents, other special matrix functions [See also 19B10, 19B14] )

 Expand all        Collapse all Results 1 - 2 of 2

1. CJM 2010 (vol 63 pp. 413)

Konvalinka, Matjaž; Skandera, Mark
 Generating Functions for Hecke Algebra Characters Certain polynomials in $n^2$ variables that serve as generating functions for symmetric group characters are sometimes called ($S_n$) character immanants. We point out a close connection between the identities of Littlewood--Merris--Watkins and Goulden--Jackson, which relate $S_n$ character immanants to the determinant, the permanent and MacMahon's Master Theorem. From these results we obtain a generalization of Muir's identity. Working with the quantum polynomial ring and the Hecke algebra $H_n(q)$, we define quantum immanants that are generating functions for Hecke algebra characters. We then prove quantum analogs of the Littlewood--Merris--Watkins identities and selected Goulden--Jackson identities that relate $H_n(q)$ character immanants to the quantum determinant, quantum permanent, and quantum Master Theorem of Garoufalidis--L\^e--Zeilberger. We also obtain a generalization of Zhang's quantization of Muir's identity. Keywords:determinant, permanent, immanant, Hecke algebra character, quantum polynomial ringCategories:15A15, 20C08, 81R50

2. CJM 2001 (vol 53 pp. 758)

Goulden, I. P.; Jackson, D. M.; Latour, F. G.
 Inequivalent Transitive Factorizations into Transpositions The question of counting minimal factorizations of permutations into transpositions that act transitively on a set has been studied extensively in the geometrical setting of ramified coverings of the sphere and in the algebraic setting of symmetric functions. It is natural, however, from a combinatorial point of view to ask how such results are affected by counting up to equivalence of factorizations, where two factorizations are equivalent if they differ only by the interchange of adjacent factors that commute. We obtain an explicit and elegant result for the number of such factorizations of permutations with precisely two factors. The approach used is a combinatorial one that rests on two constructions. We believe that this approach, and the combinatorial primitives that have been developed for the cut and join'' analysis, will also assist with the general case. Keywords:transitive, transposition, factorization, commutation, cut-and-joinCategories:05C38, 15A15, 05A15, 15A18
 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2017 : https://cms.math.ca/