An involution for the Gauss identity

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:102

Article

Chen, WYC ; Hou, QH ; Lascoux, A

关键词: involution;    Ferrers diagram;    Gauss identity;    Gauss coefficients;    q-Kummer identity;   

DOI  :  10.1016/S0097-3165(03)00043-8

来源: Elsevier

【 摘 要 】

We present an involution for a classical identity on the alternate sum of the Gauss coefficients in terms of the traditional Ferrers diagram. It turns out that the refinement of our involution with restrictions on the height of Ferrers diagram implies a generalization of the Gauss identity, which is a terminating form of the q-Kummer identity. Furthermore, we extend the Gauss identity to the pth root of unity. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

Free