منابع مشابه
Counting Partitions of Graphs
Recently, there has been much interest in studying certain graph partitions that generalize graph colourings and homomorphisms. They are described by a pattern, usually viewed as a symmetric {0, 1, ∗}matrix M . Existing results focus on recognition algorithms and characterization theorems for graphs that admit such M -partitions, or M partitions in which vertices of the input graph G have lists...
متن کاملCounting Partitions on the Abacus
In 2003, Maróti showed that one could use the machinery of l-cores and l-quotients of partitions to establish lower bounds on p(n), the number of partitions of n. In this paper we explore these ideas in the case l = 2, using them to give a largely combinatorial proof of an effective upper bound on p(n), and to prove asymptotic formulae for the number of self-conjugate partitions, and the number...
متن کاملCounting Even and Odd Partitions
1. Introduction. It is a lovely fact that n] = f1; 2; : : : ; ng, n 1, has as many subsets X with an even cardinality jXj as those with an odd cardinality, namely 2 n?1 of both. To prove it, pair every subset X with X 1 where X 1 is Xnf1g if 1 2 X and X f1g if 1 6 2 X. Then X 7 ! X 1 is an involution that changes the parity of jXj and the result follows. More generally, in enumerative combinato...
متن کاملCounting Partitions of a Fixed Genus
We show that, for any fixed genus g, the ordinary generating function for the genus g partitions of an n-element set into k blocks is algebraic. The proof involves showing that each such partition may be reduced in a unique way to a primitive partition and that the number of primitive partitions of a given genus is finite. We illustrate our method by finding the generating function for genus 2 ...
متن کاملCounting Connected Set Partitions of Graphs
Let G = (V,E) be a simple undirected graph with n vertices then a set partition π = {V1, . . . , Vk} of the vertex set of G is a connected set partition if each subgraph G[Vj ] induced by the blocks Vj of π is connected for 1 ≤ j ≤ k. Define qi(G) as the number of connected set partitions in G with i blocks. The partition polynomial is Q(G,x) = ∑n i=0 qi(G)x . This paper presents a splitting ap...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2011
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/24/9/001