A bijection between irreducible k-shapes and surjective pistols of height k-1

作者：Bigeni Ange^*

来源：Discrete Mathematics, 2015, 338(8): 1432-1448.

DOI：10.1016/j.disc.2015.03.013

• Genocchi numbers
• Gandhi polynomials
• Irreducible k-shapes
• Surjective pistols

This paper constructs a bijection between irreducible k-shapes and surjective pistols of height k - 1, which carries the "free k-sites" to the fixed points of surjective pistols. It confirms a conjecture of Hivert and Mallet (FPSAC 2011) that the number of irreducible k-shapes is the Genocchi number G(2k), and, with precision, that the irreducible k-shapes (with k >= 2) generate the Gandhi polynomial Q(2k-2) (X) with respect to the statistic of free k-sites.

• 出版日期2015-8-6