Pushes in words-a primitive sorting algorithm


  • Margaret Archibald University of the Witwatersrand
  • Aubrey Blecher University of the Witwatersrand
  • Charlotte Brennan University of the Witwatersrand
  • Arnold Knopfmacher University of the Witwatersrand
  • Toufik Mansour University of Haifa


words, generating functions, sorting, asymptotics


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.

Author Biography

Charlotte Brennan, University of the Witwatersrand

Mathematics, Associate Professor


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