منابع مشابه
Comparison of Distance Indices Between Partitions
In this paper, we compare several distance indices between partitions on the same set. First, we build a set Pk(P ) of partitions close to each others by applying to an initial partition P , k transfers of one element from its class to another. Then we compare the distributions of several indices of distance between partitions of Pk(P ).
متن کاملParity results for 15-core partitions
We find some interesting congruences modulo 2 for 13-core partitions.
متن کاملElementary Proofs of Parity Results for 5-regular Partitions
In a recent paper, Calkin et al. [N. Calkin, N. Drake, K. James, S. Law, P. Lee, D. Penniston and J. Radder, ‘Divisibility properties of the 5-regular and 13-regular partition functions’, Integers 8 (2008), #A60] used the theory of modular forms to examine 5-regular partitions modulo 2 and 13-regular partitions modulo 2 and 3; they obtained and conjectured various results. In this note, we use ...
متن کاملOn partitions into four distinct squares of equal parity
In recent work [1,2], we studied p4 (n), the number of partitions of n into four squares. We found the generating function for p4 (n), and showed that the numbers p4 (n) possess some (rare) arithmetic properties. In this paper we make a study of what we will call p4e(n) and p4o(n), the number of partitions of n into four distinct even (respectively odd) squares. We shall also have reason to con...
متن کاملPartitions weighted by the parity of the crank
Abstract. A partition statistic ‘crank’ gives combinatorial interpretations for Ramanujan’s famous partition congruences. In this paper, we establish an asymptotic formula, Ramanujan type congruences, and q-series identities that the number of partitions with even crank Me(n) minus the number of partitions with odd crank Mo(n) satisfies. For example, we show that Me(5n + 4)− Mo(5n + 4) ≡ 0 (mod...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2010
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa144-2-1