Partitions of Products
نویسندگان
چکیده
منابع مشابه
Circuit 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...
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The principal result of the paper is that, if r < u and (A¡)i<r is a partition of u, then there exist i < r and infinite subsets B and C of to such that 2 F e A¡ and IIG G A¡ whenever F and G are finite nonempty subsets of B and C respectively. Conditions on the partition are obtained which are sufficient to guarantee that B and C can be chosen equal in the above statement, and some related fin...
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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.
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A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
متن کاملIdomatic partitions of direct products of complete graphs
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1981
ISSN: 0002-9947
DOI: 10.2307/1998670