TY - JOUR
T1 - Combinatorial remarks about a "remarkable identity"
AU - Olsson, Jørn B.
AU - Sellers, James A.
PY - 2012
Y1 - 2012
N2 - 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.
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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U2 - 10.4169/math.mag.85.4.283
DO - 10.4169/math.mag.85.4.283
M3 - Article
AN - SCOPUS:84867775092
SN - 0025-570X
VL - 85
SP - 283
EP - 288
JO - Mathematics Magazine
JF - Mathematics Magazine
IS - 4
ER -