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Generalized ballot sequences are ascent sequences

Dukes, Mark (2016) Generalized ballot sequences are ascent sequences. Australasian Journal of Combinatorics, 64 (1). pp. 61-63. ISSN 1034-4942

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Abstract

Ascent sequences were introduced by the author (in conjunction with others) to encode a class of permutations that avoid a single length- three bivincular pattern, and were the central object through which other combinatorial correspondences were discovered. In this note we prove the non-trivial fact that generalized ballot sequences are ascent sequences.