Generalized pattern matching conditions for Ck ≀  Sn

Sergey Kitaev; Andrew Niedermaier; Jeffrey Remmel; Manda Riehl

doi:10.1155/2013/634823

Generalized pattern matching conditions for C_k ≀ S_n

Sergey Kitaev, Andrew Niedermaier, Jeffrey Remmel, Manda Riehl

Research output: Contribution to journal › Article › peer-review

33 Downloads (Pure)

Abstract

We derive several multivariable generating functions for a generalized pattern-matching condition on the wreath product C_k ≀ S_n of the cyclic group C_kand the symmetric group S_n In particular, we derive the generating functions for the number of matches that occur in elements of C_k ≀ S_nfor 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 C_k ≀ S_n. Our research leads to connections to many known objects/structures yet to be explained combinatorially.

Original language	English
Article number	634823
Number of pages	21
Journal	ISRN Combinatorics
Volume	2013
DOIs	https://doi.org/10.1155/2013/634823
Publication status	Published - 13 Feb 2013

Keywords

pattern matching conditions
permutations
symmetric functions
wreath products
cyclic groups

Access to Document

10.1155/2013/634823Licence: CC BY 3.0

Kitaev-etal-ISRN-C-2013-Generalized-pattern-matching-conditionsFinal published version, 2.22 MBLicence: CC BY 3.0

Cite this

@article{db413b06fe284cd683d88e87a8f4a1b7,

title = "Generalized pattern matching conditions for Ck ≀ Sn",

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.",

keywords = "pattern matching conditions, permutations, symmetric functions, wreath products, cyclic groups",

author = "Sergey Kitaev and Andrew Niedermaier and Jeffrey Remmel and Manda Riehl",

year = "2013",

month = feb,

day = "13",

doi = "10.1155/2013/634823",

language = "English",

volume = "2013",

journal = "ISRN Combinatorics",

}

TY - JOUR

T1 - Generalized pattern matching conditions for Ck ≀ Sn

AU - Kitaev, Sergey

AU - Niedermaier, Andrew

AU - Remmel, Jeffrey

AU - Riehl, Manda

PY - 2013/2/13

Y1 - 2013/2/13

N2 - 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.

AB - 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.

KW - pattern matching conditions

KW - permutations

KW - symmetric functions

KW - wreath products

KW - cyclic groups

U2 - 10.1155/2013/634823

DO - 10.1155/2013/634823

M3 - Article

VL - 2013

JO - ISRN Combinatorics

JF - ISRN Combinatorics

M1 - 634823

ER -

Generalized pattern matching conditions for Ck ≀ Sn

Abstract

Keywords

Access to Document

Fingerprint

Cite this

Generalized pattern matching conditions for C_k ≀ S_n