Partitions with Equal Products
نویسندگان
چکیده
منابع مشابه
On partitions into four distinct squares of equal parity
In recent work [1,2], we studied p4 (n), the number of partitions of n into four squares. We found the generating function for p4 (n), and showed that the numbers p4 (n) possess some (rare) arithmetic properties. In this paper we make a study of what we will call p4e(n) and p4o(n), the number of partitions of n into four distinct even (respectively odd) squares. We shall also have reason to con...
متن کاملFurther results for partitions into four squares of equal parity
We prove several results dealing with various counting functions for partitions of an integer into four squares of equal parity. Some are easy consequences of earlier work, but two are new and surprising. That is, we show that the number of partitions of 72n+60 into four odd squares (distinct or not) is even.
متن کاملCircuit partitions and #P-complete products of inner products
We present a simple, natural #P -complete problem. Let G be a directed graph, and let k be a positive integer. We define q(G; k) as follows. At each vertex v, we place a k-dimensional complex vector xv. We take the product, over all edges (u, v), of the inner product 〈xu, xv〉. Finally, q(G; k) is the expectation of this product, where the xv are chosen uniformly and independently from all vecto...
متن کاملMonochromatic Sums Equal to Products in N
Csikvári, Gyarmati, and Sárközy asked whether, whenever the set N of positive integers is finitely colored, there must exist monochromatic a, b, c, and d such that a + b = cd and a �= b. We provide an affirmative answer, showing that a much stronger statement is true.
متن کاملLecture hall partitions and the wreath products
It is shown that statistics on the wreath product groups, Ck oSn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck oSn. Finally, some new statistics on Ck oSn are introduced, inspired by lecture hall theory, and their distributions are derived.
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: Proceedings of the American Mathematical Society
سال: 1964
ISSN: 0002-9939
DOI: 10.2307/2034923