Generalized pattern matching conditions for Ck ≀  Sn

Sergey Kitaev, Andrew Niedermaier, Jeffrey Remmel, Manda Riehl

Research output: Contribution to journalArticle

9 Downloads (Pure)

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

Fingerprint

Pattern Matching
Symmetric Functions
Generating Function
Wreath Product
Homomorphisms
Analogue
Ring

Keywords

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

Cite this

Kitaev, Sergey ; Niedermaier, Andrew ; Remmel, Jeffrey ; Riehl, Manda. / Generalized pattern matching conditions for Ck ≀  Sn. In: ISRN Combinatorics. 2013 ; Vol. 2013.
@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 = "2",
day = "13",
doi = "10.1155/2013/634823",
language = "English",
volume = "2013",
journal = "ISRN Combinatorics",
issn = "2090-8911",

}

Generalized pattern matching conditions for Ck ≀  Sn. / Kitaev, Sergey; Niedermaier, Andrew; Remmel, Jeffrey; Riehl, Manda.

In: ISRN Combinatorics, Vol. 2013, 634823, 13.02.2013.

Research output: Contribution to journalArticle

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

SN - 2090-8911

M1 - 634823

ER -