Did you mean: A short note on the over partition function.
An overpartition of is a non-increasing sequence of natural numbers whose sum is in which the first occurrence of a number may be overlined. Let p ¯ ( n ) denote the number of overpartitions of an integer . For convenience, define p ¯ ( 0 ) = 1 .
Apr 28, 2009
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Jun 27, 2008 · An overpartition of n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a.
which can be understood as a convolution product between partitions into distinct parts (the overlined terms) and ordinary partitions (the rest).
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In this brief note, we give a combinatorial proof of a variation of Gauss's q-binomial theorem, and we determine arithmetic properties of the overpartition ...
This overpartition is put under the Durfee rectangle. Each overlined part decreases the rank by 1 and each part increases the number of parts by 1.
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Sep 28, 2004 · An overpartition of n is an ordered sequence of nonincreasing integers that sum to n, where the first occurrence of each distinct integer may be ...
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Jan 13, 2023 · An overpartition of a positive integer n is a partition of n in which the first occurrence of a number can be overlined. Example, for n = 3 has ...
Feb 28, 2024 · Introduction. An overpartition of n is a partition where the first occurrence of each integer may be overlined. For example, there are 14 ...
Abstract. We study overpartitions where the difference between two successive parts may be odd only if the larger part is overlined, and use q-difference ...
An overpartition of n is a non-increasing sequence of natural numbers whose sum is n in which the first occurrence of a number may be overlined.
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