منابع مشابه
Restricted integer partition functions
For two sets A and M of positive integers and for a positive integer n, let p(n,A,M) denote the number of partitions of n with parts in A and multiplicities in M , that is, the number of representations of n in the form n = ∑ a∈Amaa where ma ∈M ∪{0} for all a, and all numbers ma but finitely many are 0. It is shown that there are infinite sets A and M so that p(n,A,M) = 1 for every positive int...
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A collection of Hardy-Ramanujan-Rademacher type formulas for restricted partition and overpartition functions is presented, framed by several biographical anecdotes.
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For two sets A and M of positive integers and for a positive integer n, let p(n,A,M) denote the number of partitions of n with parts in A and multiplicities in M , that is, the number of representations of n in the form n = � a∈A maa where ma ∈ M ∪{0} for all a, and all numbers ma but finitely many are 0. It is shown that there are infinite sets A and M so that p(n,A,M) = 1 for every positive i...
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متن کاملThe topology of restricted partition posets
For each composition ~c we show that the order complex of the poset of pointed set partitions Π• ~c is a wedge of β(~c) spheres of the same dimensions, where β(~c) is the number of permutations with descent composition ~c. Furthermore, the action of the symmetric group on the top homology is isomorphic to the Specht module S where B is a border strip associated to the composition ~c. We also st...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1993
ISSN: 0022-314X
DOI: 10.1006/jnth.1993.1074