منابع مشابه
On the identities of modulo-p partitions
Some identities between partitions and compositions were obtained in the literature. As a natural extension, we introduce and study modulo-p partitions, where p is a positive integer. Moreover, several recurrence relations and some sufficient conditions for the existence of modulo-p partitions are given, respectively. In addition, we obtain some identities of modulo-p partitions. In the end, us...
متن کاملThe ranks of the classes of $A_{10}$
Let $G $ be a finite group and $X$ be a conjugacy class of $G.$ The rank of $X$ in $G,$ denoted by $rank(G{:}X),$ is defined to be the minimal number of elements of $X$ generating $G.$ In this paper we establish the ranks of all the conjugacy classes of elements for simple alternating group $A_{10}$ using the structure constants method and other results established in [A.B.M. Bas...
متن کاملOn the Positive Moments of Ranks of Partitions
By introducing k-marked Durfee symbols, Andrews found a combinatorial interpretation of 2k-th symmetrized moment η2k(n) of ranks of partitions of n in terms of (k + 1)-marked Durfee symbols of n. In this paper, we consider the k-th symmetrized positive moment η̄k(n) of ranks of partitions of n which is defined as the truncated sum over positive ranks of partitions of n. As combintorial interpret...
متن کاملA Bijection for Partitions with All Ranks at Least tSylvie
It follows from work of Andrews and Bressoud that for t 1, the number of partitions of n with all successive ranks at least t is equal to the number of partitions of n with no part of size 2?t. We give a simple bijection for this identity which generalizes a result of Cheema and Gordon for 2-rowed plane partitions. The bijection yields several reenements of the identity when the partition count...
متن کاملA Bijection for Partitions with All Ranks at Least t
It follows from work of Andrews and Bressoud that for t the number of parti tions of n with all successive ranks at least t is equal to the number of partitions of n with no part of size t We give a simple bijection for this identity which generalizes a result of Cheema and Gordon for rowed plane partitions The bijection yields several re nements of the identity when the partition counts are pa...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2013
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.05.014