q-Stirling numbers arising from vincular patterns

10/14/2018

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by   Joanna N. Chen, et al.

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The distribution of certain Mahonian statistic (called BAST) introduced by Babson and Steingrímsson over the set of permutations that avoid vincular pattern 132, 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 BAST and its reverse complement STAT is derived as well.