Counting Berg partitions
نویسندگان
چکیده
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...
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: Nonlinearity
سال: 2011
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/24/9/001