منابع مشابه
Distinct Parts Partitions without Sequences
Partitions without sequences of consecutive integers as parts have been studied recently by many authors, including Andrews, Holroyd, Liggett, and Romik, among others. Their results include a description of combinatorial properties, hypergeometric representations for the generating functions, and asymptotic formulas for the enumeration functions. We complete a similar investigation of partition...
متن کاملA note on partitions into distinct parts and odd parts
Bousquet-Mélou and Eriksson showed that the number of partitions of n into distinct parts whose alternating sum is k is equal to the number of partitions of n into k odd parts, which is a refinement of a well-known result by Euler. We give a different graphical interpretation of the bijection by Sylvester on partitions into distinct parts and partitions into odd parts, and show that the bijecti...
متن کاملPartitions and Overpartitions with Attached Parts
We show how to interpret a certain q-series as a generating function for overpartitions with attached parts. A number of families of partition theorems follow as corollaries.
متن کاملThe Arithmetic of Partitions into Distinct Parts
so that Q(n) is odd if and only if n is a pentagonal number. This fact was generalized by Gordon and Ono [4], who demonstrated that for any positive integer k almost all values of Q(n) are divisible by 2k, and by Ono and Penniston [7], who found an exact formula for Q(n) modulo 8. Their techniques do not apply to odd primes, however, and for these primes the situation seems to be more difficult...
متن کاملPartitions of rt(t, n) into parts
Szekeres proved, using complex analysis, an asymptotic formula for the number of partitions of n into at most k parts. Canfield discovered a simplification of the formula, and proved it without complex analysis. We re-prove the formula, in the asymptotic regime when k is at least a constant times √ n, by showing that it is equivalent to a local central limit theorem in Fristedt’s model for rand...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2004
ISSN: 1246-7405
DOI: 10.5802/jtnb.464