Parity indices of partitions
نویسندگان
چکیده
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 ).
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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...
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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