M. Archibald, A. Blecher, C. Brennan, A. Knopfmacher, T. Mansour

Research output: Contribution to journalArticlepeer-review


We define the statistic of a push for words on an alphabet [k] and use this to obtain a generating function measuring the degree to which an arbitrary word deviates from sorted order. Several subsidiary concepts are investigated: the number of cells that are not pushed, the number of already sorted columns, the number of cells that coincide before and after pushing, the fixed cells in words and finally, the frictionless pushes.

Original languageEnglish
Pages (from-to)56-69
Number of pages14
JournalContributions to Discrete Mathematics
Issue number1
StatePublished - 2022

Bibliographical note

Funding Information:
Received by the editors March 14, 2019, and in revised form July 23, 2021. 2000 Mathematics Subject Classification. Primary: 05A15, Secondary: 05A05. Key words and phrases. words, generating function, sorting, asymptotics. This material is based upon work supported by the National Research Foundation under grant numbers 89147, 86329 and 81021 for M. Archibald, C. Brennan and A. Knopfmacher respectively.

Publisher Copyright:
© 2022 University of Calgary. All rights reserved.


  • asymptotics
  • generating function
  • sorting
  • words

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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