Guodong Liu Department of Mathematics, Huizhou University, Huizhou, Guangdong 516015, China Correspondence should be addressed to Guodong Liu, [email protected] Received 18 June 2009; Accepted 12 August 2009 Recommended by Leonid Berezansky An explicit formula, the generalized Genocchi numbers, was established and some identities and congruences involving the Genocchi numbers, the Bernoul...

We use the level 12 theory of theta functions to derive hypergeometric transformation formulas and show that forty-two functions are equal. We discuss applications to Ramanujan’s series for 1/π and show how to obtain iterations that converge rapidly to 1/π. CUBIC THETA FUNCTIONS A GLIMPSE S.Bhargava [email protected] Department of Studies in Mathematics University of Mysore Manasagango...

Let e 2n denote the subposet obtained by selecting even ranks in the partition lattice 2n : We show that the homology of e 2n has dimension (2n)! 2 2n?1 E 2n?1 ; where E 2n?1 is the tangent number. It is thus an integral multiple of both the Genocchi number and an Andr e or simsun number. Using the general theory of rank-selected homology representations developed in Su], we show that, for the ...

Let Pe2n denote the subposet obtained by selecting even ranks in the partition lattice P2n. We show that the homology of Pe2n has dimension (2n)! E2n-1, where E2n-1 is the tangent number. It is thus an integral multiple of both the Genocchi number and an Andre or simsun number. Using the general theory of rankselected homology representations developed in [22], we show that, for the special cas...

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. The bijection confirms a conjecture of Hivert and Mallet (FPSAC 2011) that the number of irreducible k-shape is counted by the Genocchi number G2k. Résumé. On construit une bijection entre les k-formes irréductibles et l...