The median Genocchi numbers, Q-analogues and continued fractions

Details The median Genocchi numbers, Q-analogues and continued fractions The median Genocchi numbers, Q-analogues and continued fractions

2011-11-03

arxiv.org/abs/1111.0740v1

Mathematics

Combinatorics

12 pages

Scientific paper

The goal of this paper is twofold. First, we review the recently developed geometric approach to the combinatorics of the median Genocchi numbers. The Genocchi numbers appear in this context as Euler characteristics of the degenerate flag varieties. Second, we prove that the generating function of the Poincar\' e polynomials of the degenerate flag varieties can be written as a simple continued fraction. We thus obtain a q-analogue and a new proof of the Viennot formula.

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