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$q$-Stirling numbers arising from vincular patterns. (arXiv:1810.06052v1 [math.CO])
来源于:arXiv
The distribution of certain Mahonian statistic (called $\mathrm{BAST}$)
introduced by Babson and Steingr\'{i}msson over the set of permutations that
avoid vincular pattern $1\underline{32}$, is shown bijectively to match the
distribution of major index over the same set. This new layer of
equidistribution is then applied to give alternative interpretations of two
related $q$-Stirling numbers of the second kind, studied by Carlitz and Gould.
An extension to an Euler-Mahonian statistic over the set of ordered partitions
presents itself naturally. During the course, a refined relation between
$\mathrm{BAST}$ and its reverse complement $\mathrm{STAT}$ is derived as well. 查看全文>>