We give a simple and natural proof of (an extension of) the identity P(k, l, n) = P2(k − 1, l − 1, n − 1). The number P(k, l, n) counts noncrossing partitions of {1, 2, . . ...
A graphical partition of the even integer n is a partition of n where each part of the partition is the degree of a vertex in a simple graph and the degree sum of the graph is n. ...
Deborah A. Frank, Carla D. Savage, James A. Seller...
In two previous papers, the study of partitions with short sequences has been developed both for its intrinsic interest and for a variety of applications. The object of this paper...
George Andrews, Henrik Eriksson, Fedor Petrov, Dan...
Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned ni numbers with ni lying in a given range. The goal is to maximize a Schur con...
F. H. Chang, H. B. Chen, J. Y. Guo, Frank K. Hwang...