Résumé : We'll begin with a short survey on orthogonal polynomials and then we'll consider the following model. If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the negative version of the number of bounded Dyck paths is the number of bounded alternating sequences. In this talk we present two methods to compute the negative versions of sequences related to moments of orthogonal polynomials. We give a combinatorial model for the negative version of the number of bounded Motzkin paths. We also prove two conjectures of Cigler and Krattenthaler on reciprocity between determinants. Joint work with Donghyun Kim, Jang Soo Kim, Minho Song, U-Keun Song.

 [Slides.pdf] [arXiv] [vidéo]

Dernière modification : Monday 18 March 2024

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