On simultaneous s-cores/t-cores
Copyright policy )On simultaneous s-cores/t-cores
In this paper, the authors investigate the question of when a partition of n∈N is an s-core and also a t-core when s and t are not relatively prime. A characterization of all such s/t-cores is given, as well as a generating function dependent upon the polynomial generating functions for s/t-cores when s and t are relatively prime. Furthermore, characterizations and generating functions are given for s/t-cores which are self-conjugate and also for (e,r)/(e′,r)-cores.
postprint
- University of Wisconsin–Stevens Point United States
- University of Hong Kong China (People's Republic of)
- California Polytechnic State University Foundation United States
- University of Wisconsin–Madison United States
- University of Hong Kong (香港大學) China (People's Republic of)
Generating functions, Combinatorial aspects of partitions of integers, Symmetric functions and generalizations, Partitions, t-cores, Characterization, partitions, generating functions, Exact enumeration problems, generating functions, Elementary theory of partitions, \(t\)-cores, Function evaluation
Generating functions, Combinatorial aspects of partitions of integers, Symmetric functions and generalizations, Partitions, t-cores, Characterization, partitions, generating functions, Exact enumeration problems, generating functions, Elementary theory of partitions, \(t\)-cores, Function evaluation
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