Báo cáo toán học: "Universally Image Partition Regularity" potx

... image partition regular if given any pair (S, A), M is image partition regular over S with respect to A. In the following discussions we shall observe that for matrices of finite order image partition ... In this paper we introduce a new notion which we call universally image partition regular matrices, which are in fact image partition regular over all semigroups and every...

Ngày tải lên: 07/08/2014, 21:21

... remark that there are 160 n-color partitions of 8 but only one partition viz., 6 2 +2 2 is relevant for Theorem 3 and none is relevant for Theorem 4. Out of 859 n-color partitions of 11, none is relevant ... has been interpreted as generating function for partitions into odd parts without gaps [5]. We in this paper use n-color partitions (also called partitions with n copies of n and studie...

Ngày tải lên: 07/08/2014, 08:20

... open questions. 2 The Main Theorem We begin with some preliminaries about partitions and their conjugates. For a given partition π with parts each  N,wedenotebyf i (π) the number of appearances ... z,y −1 ). (15) Proof. We shall in the following be dealing with partitions whose parts are all  some given N.Welet¯π be that partition made up of the parts of π that are <N. In light of (1...

Ngày tải lên: 07/08/2014, 08:22

... Theorem 1.4 from the following more general statement. Theorem 2.1 Let G be a bipartite graph with partition classes E G and O G , H an arbitrary graph and L = L(G, H) a list set. Suppose that there ... G, |Hom(G, H)|≤|Hom(K d,d ,H)| N 2d where K d,d is the complete bipartite graph with d vertices in each partition class. In [4] Theorem 1.1 is extended to a result on weighted graph homomo...

Ngày tải lên: 07/08/2014, 13:21

... Wesaythatthetypeofthismonomial is a set partition A ∈ Π m with the property that i a = i b if and only if a and b are in the same block of the set partition. This set partition is denoted as ∇(i 1 ,i 2 , ... consider the partition lattice algebras. For a fixed n consider the vector space (kΠ n , ∧) formally spanned by the set partitions of n. The multiplication is given by the operation...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 15:20

... one-factor of a graph G is a spanning regular subgraph of degree one. A one-factorization of G is a partition of E(G) into one-factors. Clearly, the rows of a Latin rectangle R correspond to the one-factors

Ngày tải lên: 07/08/2014, 06:20

... misses some edges at a distance of 1, 2 and 3 from e.) Consequently distinct edges have distinct images under i S , and so this function is injective. Hence I S (S)=|EP|, as claimed. It follows ... 2 n−2 contain both X and Y . The hypothesis concerning I S (S) shows that at least one of these is the image under i S of some s ∈ S.In other words, X ∈ i S (s) and Y ∈ i S (s). It follows that s...

Ngày tải lên: 07/08/2014, 06:20

... VbVrV HV bVHVHHVrVHHHVH ∈ L cc 2 (8; 2) with peak set {(0, 2), (1, 4), (2, 5), (4, 7), (7, 8)}. The image path is f(R)= V V V VbHV V rHHVbHHHVV rHH ∈ L c 2 (8; 2) where now the colors b and r label peaks.

Ngày tải lên: 07/08/2014, 06:20

... n,letr k be the number of partitions of the vertex set into k nonempty parts (colour classes) such that the colouring constraint is satisfied on each C- and D-edge. We call these partitions feasible.Thusr k is ... of partitions of V (G) into k non-empty sets that describe a good-colouring of the mixed hypergraph G.LetS(n, k) denote the Stirling numbers of the second kind, i.e. the number of wa...

Ngày tải lên: 07/08/2014, 06:22