Name
Abstract | ||
|---|---|---|
In his memoir in 1984, George E. Andrews introduces many general classes of Frobenius partitions (simply F-partitions). Especially, he focuses his interest on two general classes of F-partitions: one is F-partitions that allow up to k repetitions of an integer in any row, and the other is F-partitions whose parts are taken from k copies of the nonnegative integers. The latter are called k colored F-partitions or F-partitions with k colors. Andrews derives the generating functions of the number of F-partitions with k repetitions and F-partitions with k colors of n and leaves their purely combinatorial proofs as open problems. The primary goal of this article is to provide combinatorial proofs in answer to Andrews' request. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0097-3165(03)00023-2 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
k color,k copy,open problem,k repetition,generating function,frobenius partition,combinatorial proof,function identity,nonnegative integer,general class,george e. andrews | Integer,Generating function,Discrete mathematics,Combinatorics,Colored,Combinatorial proof,Mathematics | Journal |
Volume | Issue | ISSN |
102 | 1 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
1 | 0.62 | 1 |
Authors | ||
1 | ||