A Note on the Geometry of Figurate Numbers. Issue 5 (28th May 2021)

• Record Type: Journal Article
• Authors: Marko, František; Cereceda, José L.
• Is Part Of: American Mathematical Monthly. Volume 128:Issue 5(2021)
• Page Start: 461
• Page End: 463
• Publication Date: 2021-05-28
• Subjects: Primary 11B83 -- Secondary 11B65 -- 11B68; Mathematics -- Periodicals; 510.5
• DOI: 10.1080/00029890.2021.1895660
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: For positive integers n and p, we give a short proof of a formula expressing n p as a linear combination of figurate numbers with coefficients given by the numbers c p, l of ( p − l ) -dimensional facets of p -dimensional simplices obtained by cutting a p -dimensional cube, where l = 0, 1, …, p − 1 . This formula was formulated as Conjecture 16 in F. Marko and S. Litvinov (2020), Geometry of figurate numbers and sums of powers of consecutive natural numbers, this Monthly, 127(1): 4–22.