English

A note on the geometry of figurate numbers

Number Theory 2020-04-10 v1

Abstract

We give a short proof of the formula np==0p1(1)cp,Fnpn^p=\sum_{\ell=0}^{p-1} (-1)^{\ell} c_{p,\ell} F^{p-\ell}_n, where FnpF^{p-\ell}_n is the figurate number and cp,c_{p,\ell} is the number of (p)(p-\ell)-dimensional facets of pp-dimensional simplices obtained by cutting the pp-dimensional cube.

Cite

@article{arxiv.2004.04678,
  title  = {A note on the geometry of figurate numbers},
  author = {Frantisek Marko},
  journal= {arXiv preprint arXiv:2004.04678},
  year   = {2020}
}
R2 v1 2026-06-23T14:45:55.270Z