An involution for the Gauss identity

  • Authors:

  • William Y. C. Chen;Qing-Hu Hou;Alain Lascoux

  • Affiliations:

  • Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, People's Republic of China;Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, People's Republic of China;Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, People's Republic of China and CNRS, Institut Gaspard Monge, Université de Marne-la-Vallée, 77454 Marne-la-Vallée ...

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2003

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Abstract

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.