Michael Albert ; Robert Brignall - $2\times 2$ monotone grid classes are finitely based

dmtcs:1325 - Discrete Mathematics & Theoretical Computer Science, February 11, 2016, Vol. 18 no. 2, Permutation Patterns 2015 - https://doi.org/10.46298/dmtcs.1325
$2\times 2$ monotone grid classes are finitely based

Authors: Michael Albert ; Robert Brignall

    In this note, we prove that all $2 \times 2$ monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This follows from a slightly more general result about certain $2 \times 2$ (generalized) grid classes having two monotone cells in the same row.


    Volume: Vol. 18 no. 2, Permutation Patterns 2015
    Section: Permutation Patterns
    Published on: February 11, 2016
    Submitted on: February 11, 2016
    Keywords: Mathematics - Combinatorics,05A05

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