Generalized pattern matching conditions for Ck ≀  Sn

Sergey Kitaev, Andrew Niedermaier, Jeffrey Remmel, Manda Riehl

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Abstract

We derive several multivariable generating functions for a generalized pattern-matching condition on the wreath product Ck ≀  Sn of the cyclic group Ck and the symmetric group Sn In particular, we derive the generating functions for the number of matches that occur in elements of Ck ≀  Sfor any pattern of length 2 by applying appropriate homomorphisms from the ring of symmetric functions over an infinite number of variables to simple symmetric function identities. This allows us to derive several natural analogues of the distribution of rises relative to the product order on elements of Ck ≀  Sn. Our research leads to connections to many known objects/structures yet to be explained combinatorially.
Original languageEnglish
Article number634823
Number of pages21
JournalISRN Combinatorics
Volume2013
DOIs
Publication statusPublished - 13 Feb 2013

Keywords

  • pattern matching conditions
  • permutations
  • symmetric functions
  • wreath products
  • cyclic groups

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