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Abstract: This paper presents a bijection between ascent sequences and upper triangularmatrices whose non-negative entries are such that all rows and columns containat least one non-zero entry. We show the equivalence of several naturalstatistics on these structures under this bijection and prove that some ofthese statistics are equidistributed. Several special classes of matrices areshown to have simple formulations in terms of ascent sequences. Binary matricesare shown to correspond to ascent sequences with no two adjacent entries thesame. Bidiagonal matrices are shown to be related to order-consecutive setpartitions and a simple condition on the ascent sequences generate this class.



Autor: Mark Dukes, Robert Parviainen

Fuente: https://arxiv.org/



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