COMBINATORIAL IDENTITIES INVOLVING THE CENTRAL COEFFICIENTS OF A SHEFFER MATRIX

Applicable Analysis and Discrete Mathematics

article

Emanuele Munarini¹ 

[1] Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32

关键词: $r$-Lah numbers;    $r$-Stirling numbers;    Appell sequences;    Sheffer sequences;    Combinatorial Identities;   

DOI  :  10.2298/AADM180226017M

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

Given m ∈ N, m ≥ 1, and a Sheffer matrix S = [sn,k]n,k≥0, we obtain the exponential generating series for the coefficients a+(m+1)na+mn −1 sa+(m+1)n,a+mn.Then, by using this series, we obtain two general combinatorial identities, and their specialization to r-Stirling, r-Lah and r-idempotent numbers. In particular, using this approach, we recover two well known binomial identities, namely Gould’s identity and Hagen-Rothe’s identity. Moreover, wegeneralize these results obtaining an exchange identity for a cross sequence(or for two Sheffer sequences) and an Abel-like identity for a cross sequence(or for an s-Appell sequence).

【 授权许可】

Unknown