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.

    Author(s):Kitaev, Sergey ORCID logoORCID: https://orcid.org/0000-0003-3324-1647, Niedermaier, Andrew, Remmel, Jeffrey and Riehl, Manda
    Item type:Article
    ID code:49883
    Keywords: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:04 Oct 2019 01:42
    URI:https://strathprints.strath.ac.uk/id/eprint/49883
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