A DIFFERENTIAL OPERATOR FOR SYMMETRICAL FUNCTIONS AND THE COMBINATORICS OF MULTIPLYING TRANSPOSITIONS

Authors
GOULDEN IP
Citation
Ip. Goulden, A DIFFERENTIAL OPERATOR FOR SYMMETRICAL FUNCTIONS AND THE COMBINATORICS OF MULTIPLYING TRANSPOSITIONS, Transactions of the American Mathematical Society, 344(1), 1994, pp. 421-440
Citations number
20
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
344
Issue
1
Year of publication
1994
Pages
421 - 440
Database
ISI
SICI code
0002-9947(1994)344:1<421:ADOFSF>2.0.ZU;2-Z
Abstract
By means of irreducible characters for the symmetric group, formulas h ave previously been given for the number of ways of writing permutatio ns in a given conjugacy class as products of transpositions. These for mulas are alternating sums of binomial coefficients and powers of inte gers. Combinatorial proofs are obtained in this paper by analyzing the action of a partial differential operator for symmetric functions.