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Abstract

Speaker: Catherine Yan, (Texas A&M University)

Title: Non-crossing and non-nesting matchings

Abstract: I will present results on the enumeration of noncrossing and nonnesting matchings. Using a bijection between complete matchings and oscillating talbeaux, we show that two statistics, the crossing number and the nesting number of complete matchings, have a symmetric joint distribution. As a corollary, the number of $k$-noncrossing matchings is equal to the number of $k$-nesting matchings.



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