Séminaire Lotharingien de Combinatoire, B76c (2017), 39 pp.

Volker Strehl

Lacunary Laguerre Series from a Combinatorial Perspective

Abstract. In recent work, Babusci, Dattoli, G\'orska, and Penson have presented a number of lacunary generating functions for the generalized Laguerre polynomials Ln(\alpha)(x), i.e., series of the type \sumn >= 0 cn L2n(\alpha)(x) tn, by a method closely related to umbral calculus. This work is complemented here, deriving many of their results by interpreting Laguerre polynomials combinatorially as enumerators for discrete structures (injective partial functions). This combinatorial view pays in that it suggests natural extensions and gives a deeper insight into the known formulas.

Received: December 21, 2016. Accepted: February 25, 2017. Final Version: March 22, 2017.

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