منابع مشابه
Partition Statistics for Cubic Partition Pairs
In this brief note, we give two partition statistics which explain the following partition congruences: b(5n + 4) ≡ 0 (mod 5), b(7n + a) ≡ 0 (mod 7), if a = 2, 3, 4, or 6. Here, b(n) is the number of 4-color partitions of n with colors r, y, o, and b subject to the restriction that the colors o and b appear only in even parts.
متن کاملRestricted 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...
متن کاملIdentically Distributed Pairs of Partition Statistics
We show that many theorems which assert that two kinds of partitions of the same integer n are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics X and Y that have identical distribution functions. The method is an extension of the principle of sieve-equivalence, and it yields simple criteria under which we can...
متن کاملArithmetic Properties of Overcubic Partition Pairs
Let b(n) denote the number of overcubic partition pairs of n. In this paper, we establish two Ramanujan type congruences and several infinite families of congruences modulo 3 satisfied by b(n). For modulus 5, we obtain one Ramanujan type congruence and two congruence relations for b(n), from which some strange congruences are derived.
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 Combinatorial Theory, Series A
سال: 1993
ISSN: 0097-3165
DOI: 10.1016/0097-3165(93)90057-f