Pushes in words-a primitive sorting algorithm
DOI:
https://doi.org/10.55016/ojs/cdm.v17i1.67951Keywords:
words, generating functions, sorting, asymptoticsAbstract
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.
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