A curious polynomial interpolation of Carlitz-Riordan's q-ballot numbers

Authors

  • Frédéric Chapoton CNRS et University Lyon 1
  • Jiang Zeng Université Claude Bernard Lyon 1

DOI:

https://doi.org/10.11575/cdm.v10i1.62222

Keywords:

q-Catalan numbers, lattice paths, q-ballot numbers

Abstract

We study a polynomial sequence Cn(x|q) defined as a solution of a q-difference equation. This sequence, evaluated at q-integers, interpolates Carlitz--Riordan's q-ballot numbers. In the basis given by some kind of q-binomial coefficients, the coefficients are again some q-ballot numbers. We obtain another curious recurrence relation for these polynomials in a combinatorial way.

Author Biographies

Frédéric Chapoton, CNRS et University Lyon 1

Institut Camille Jordan

Université Claude Bernard Lyon 1

Bâtiment Braconnier

21 Avenue Claude Bernard

F-69622 VILLEURBANNE Cedex

Jiang Zeng, Université Claude Bernard Lyon 1

Institut Camille Jordan

Université Claude Bernard Lyon 1

Bâtiment Braconnier

21 Avenue Claude Bernard

F-69622 VILLEURBANNE Cedex

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Published

2015-07-31

Issue

Vol. 10 No. 1 (2015)

Section

Articles

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