The median Genocchi numbers, Q-analogues and continued fractions

2011/11/03 by Evgeny Feigin, Feigin, Evgeny · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1111.0740

openalex publication_date 2011/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. As an application we prove that the Poincar' e polynomials coincide with the q-version of the normalized median Genocchi numbers introduced by Han and Zeng.

Cited by

• PrIncipal quiver Grassmannians: conjectures

Related

• Combinatorial study of the Dellac configurations and the q-extended normalized median Genocchi numbers
• Degenerate flag varieties and the median Genocchi numbers
• A note on the q-Genocchi numbers and polynomials
• Cycles of even-odd drop permutations and continued fractions of Genocchi numbers
• Gamma-positivity for a Refinement of Median Genocchi Numbers