A Note on the Geometry of Figurate Numbers

František Marko; José L. Cereceda

doi:10.1080/00029890.2021.1895660

A Note on the Geometry of Figurate Numbers

František Marko
, José L. Cereceda

Penn State Hazleton

Research output: Contribution to journal › Comment/debate › peer-review

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 (Formula presented.) of (Formula presented.) -dimensional facets of p-dimensional simplices obtained by cutting a p-dimensional cube, where (Formula presented.). 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.

Original language	English (US)
Pages (from-to)	461-463
Number of pages	3
Journal	American Mathematical Monthly
Volume	128
Issue number	5
DOIs	https://doi.org/10.1080/00029890.2021.1895660
State	Published - 2021

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1080/00029890.2021.1895660

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title = "A Note on the Geometry of Figurate Numbers",

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AU - Cereceda, José L.

N1 - Publisher Copyright: ©, THE MATHEMATICAL ASSOCIATION OF AMERICA.

PY - 2021

Y1 - 2021

N2 - For positive integers n and p, we give a short proof of a formula expressing np as a linear combination of figurate numbers with coefficients given by the numbers (Formula presented.) of (Formula presented.) -dimensional facets of p-dimensional simplices obtained by cutting a p-dimensional cube, where (Formula presented.). 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.

AB - For positive integers n and p, we give a short proof of a formula expressing np as a linear combination of figurate numbers with coefficients given by the numbers (Formula presented.) of (Formula presented.) -dimensional facets of p-dimensional simplices obtained by cutting a p-dimensional cube, where (Formula presented.). 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.

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M3 - Comment/debate

AN - SCOPUS:85105188757

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EP - 463

JO - American Mathematical Monthly

JF - American Mathematical Monthly

IS - 5

ER -

A Note on the Geometry of Figurate Numbers

Abstract

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