Báo cáo toán học: "On counting permutations by pairs of congruence classes of major index" doc

... electronic journal of combinatorics 9 (2002), #R21 10 On counting permutations by pairs of congruence classes of major index H ´ el ` ene Barcelo and Robert Maule Sheila Sundaram Department of Mathematics ... give a constructive proof of an equivalent restatement of Propo- sition 2.5, by looking at the circular classes of permutations τ ∈ S n which fix n. Note...

Ngày tải lên: 07/08/2014, 06:23

... Consider a copy of H in G. It contains at least one of the components of order m, thus it has at least two vertices of the same color. Therefore there is no rainbow induced subgraph of G isomorphic ... isomorphic. Consider S, a neighborhood of a vertex v of maximum degree in G. Then, all subsets of S of size k − 2 induce isomorphic graphs. Therefore, if |S|≥k we have, by P...

Ngày tải lên: 07/08/2014, 13:21

... versions of the conjecture are equivalent. Here is some background information on the current status of the Stanley-Wilf conjecture. Represent σ ∈S k by the word σ(1) σ(2) ···σ(k). For the case of the ... −1) 2 achieved by the identity permutation. Conjecture 1. ($100.00) For all σ ∈S k and n ≥ 1, F (n, σ) ≤ (k −1) 2n . The problem of the shortest common superpattern. Define G(n, k...

Ngày tải lên: 07/08/2014, 06:22

... new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length n and the set of parking functions of length ... parking functions by pairs of permutations Yurii Burman Independent University of Moscow, 121002, 11, B.Vlassievsky per., Moscow, Russia burman@mccme.ru Michael Shapiro Dep...

Ngày tải lên: 07/08/2014, 07:21

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Ngày tải lên: 05/08/2014, 15:20

... . ∪ S k of the set of columns of the matrix A such that elements of S 1 add up to 0 and that, for any j ∈ {2, . . . k}, the sum of all elements of S j is a rational li near combination of the ... the degree of partition regularity of the given recurrence for s-term sequences and denoted by k 0 (s; a, b, c). We note that the problem of finding the degree of partition reg...

Ngày tải lên: 08/08/2014, 12:22

... dimension of G, denoted by β(G), is the minimum card i nality of a resolving set of G. The following result was independently proved by Harary [13], Erwin and Harary [11] (using fixing sets instead of ... set of G, if every vertex is uniquely determined by its vector of distances to the vertices of S. A resolving set S of minimum cardinality is a metric basis, and |S| is...

Ngày tải lên: 08/08/2014, 12:22

... degree in G of a vertex v is denoted by d G (v), or simply d(v), and the number of neighbors of v in a subset S of V by d S (v). A subset S of vertices is dominating if every vertex of V \S has ... balanced tree S by attaching a set L(u) of d S (u) leaves at each vertex u of S. Let I be a maximal independent set of T and q the number of components of the forest ind...

Ngày tải lên: 07/08/2014, 21:20

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