Generalized pattern matching conditions for Ck ≀ Sn
Kitaev, Sergey and Niedermaier, Andrew and Remmel, Jeffrey and Riehl, Manda (2013) Generalized pattern matching conditions for Ck ≀ Sn. ISRN Combinatorics, 2013. 634823.
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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 ≀ Sn for 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.
ORCID iDs
Kitaev, Sergey
ORCID: https://orcid.org/0000-0003-3324-1647, Niedermaier, Andrew, Remmel, Jeffrey and Riehl, Manda;
Item type: Article ID code: 49883 Dates: DateEvent13 February 2013PublishedKeywords: pattern matching conditions, permutations, symmetric functions, wreath products, cyclic groups, Electronic computers. Computer science Subjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 17 Oct 2014 10:44 Last modified: 02 Apr 2021 00:41 URI: https://strathprints.strath.ac.uk/id/eprint/49883
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