منابع مشابه
Dissecting the Stanley partition function
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...
متن کاملOn 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).
متن کاملThe Andrews-Stanley partition function and Al-Salam-Chihara polynomials
We show that the generating function ∑ ω(λ) where ω(λ) denotes the four parameter weight ω(λ) = a ∑ i≥12i−1b ∑ i≥12i−1c ∑ i≥12id ∑ i≥12i, and the sum runs over all ordinary or strict partitions λ with parts each ≤ N , is expressed by the Al-Salam Chihara polynomials. As a corollary we prove C. Boulet’s results when λ runs over all ordinary or strict partitions. In the last section we study the ...
متن کاملOn partition functions of Andrews and Stanley
G. E. Andrews has established a refinement of the generating function for partitions π according to the numbers O(π) and O(π′) of odd parts in π and the conjugate of π, respectively. In this paper, we derive a refined generating function for partitions into at most M parts less than or equal to N , which is a finite case of Andrew’s refinement.
متن کاملThe Partition Function of Andrews and Stanley and Al-Salam-Chihara Polynomials
For any partition λ let ω(λ) denote the four parameter weight ω(λ) = a P
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2005
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2005.03.001