Bijective recurrences for Schroeder triangles and Comtet statistics

Abstract: In this talk, we bijectively establish recurrence relations for two triangular arrays, relying on their interpretations in terms of Schroeder paths (resp. little Schroeder paths) with given length and number of hills. The row sums of these two triangles produce the large (resp. little) Schroeder numbers. On the other hand, it is well-known that the large Schroeder numbers also enumerate separable permutations. This propelled us to reveal the connection with a lesser-known permutation statistic, called initial ascending run (iar), whose distribution on separable permutations is shown to be given by the first triangle as well. A by-product of this result is that "iar" is equidistributed over separable permutations with "comp", the number of components of a permutation. We call such statistics Comtet and we briefly mention further work concerning Comtet statistics on various classes of pattern avoiding permutations. The talk is based on joint work with Zhicong Lin and Yaling Wang.

classical analysis and ODEscombinatoricsnumber theory

Audience: researchers in the topic

Special Functions and Number Theory seminar

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