English

Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas

Combinatorics 2011-03-25 v1

Abstract

Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler's pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this multivariate series identity and two formulas of Lucas. Finally we give a combinatorial proof of Lucas' formulas.

Keywords

Cite

@article{arxiv.0707.4328,
  title  = {Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas},
  author = {Victor J. W. Guo and Jiang Zeng},
  journal= {arXiv preprint arXiv:0707.4328},
  year   = {2011}
}

Comments

11 pages, to appear in Discrete Mathematics. See also http://math.univ-lyon1.fr/~guo

R2 v1 2026-06-21T09:02:51.438Z