On a Partition Function of Richard Stanley
نویسندگان
چکیده
منابع مشابه
On a Partition Function of Richard Stanley
In this paper, we examine partitions π classified according to the number r(π) of odd parts in π and s(π) the number of odd parts in π′, the conjugate of π. The generating function for such partitions is obtained when the parts of π are all 5 N . From this a variety of corollaries follow including a Ramanujan type congruence for Stanley’s partition function t(n).
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Let p(n) denote the number of unrestricted partitions of n. For i = 0, 2, let pi(n) denote the number of partitions π of n such that O(π)−O(π) ≡ i (mod 4). Here O(π) denotes the number of odd parts of the partition π and π is the conjugate of π. R. Stanley [13], [14] derived an infinite product representation for the generating function of p0(n)− p2(n). Recently, H. Swisher [15] employed the ci...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2004
ISSN: 1077-8926
DOI: 10.37236/1858