A note on the geometry of figurate numbers

2020/04/04 by Frantisek Marko, Marko, Frantisek
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.2004.04678

arxiv created 2020/04/04 · arxiv updated 2020/04/10

Abstract

We give a short proof of the formula n^p=∑_ℓ=0^p-1 (-1)^ℓ c_p,ℓ F^p-ℓ_n, where F^p-ℓ_n is the figurate number and c_p,ℓ is the number of (p-ℓ)-dimensional facets of p-dimensional simplices obtained by cutting the p-dimensional cube.

Related

• Figurate numbers and sums of powers of integers
• On sums of figurate numbers by using techniques of poset representation theory
• An improvement on the number of simplices in \mathbbF_q^d
• On The Log-Concavity of Polygonal Figurate Number Sequences
• Figurate numbers, forms of mixed type and their representation numbers