Combinatorial remarks about a "remarkable identity"

Jørn Børling Olsson; James A. Sellers

Combinatorial remarks about a "remarkable identity"

Bidragets oversatte titel: Kombinatorsike bemærkninger om en "bemærkelsesværdig identitet"

Institut for Matematiske Fag

Abstract

In the June 2012 issue of this Magazine, Frumosu and Teodorescu-Frumosu proved that, for all integers m ≥ 2, where the inner sum is taken over all p-term ordered partitions of m. Their proof is calculus-based, relying on power series manipulations. In this note, we provide a combinatorial proof of this identity (which they requested at the end of their article) and we use the insights gained via this argument to prove other results of a similar type.

Bidragets oversatte titel	Kombinatorsike bemærkninger om en "bemærkelsesværdig identitet"
Originalsprog	Engelsk
Tidsskrift	Mathematics Magazine
Vol/bind	85
Udgave nummer	4
Sider (fra-til)	283-288
ISSN	0025-570X
Status	Udgivet - okt. 2012

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http://www.jstor.org/stable/10.4169/math.mag.85.4.283

Citationsformater

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AB - In the June 2012 issue of this Magazine, Frumosu and Teodorescu-Frumosu proved that, for all integers m ≥ 2, where the inner sum is taken over all p-term ordered partitions of m. Their proof is calculus-based, relying on power series manipulations. In this note, we provide a combinatorial proof of this identity (which they requested at the end of their article) and we use the insights gained via this argument to prove other results of a similar type.

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SN - 0025-570X

VL - 85

SP - 283

EP - 288

JO - Mathematics Magazine

JF - Mathematics Magazine

IS - 4

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Combinatorial remarks about a "remarkable identity"

Abstract

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