Báo cáo toán học: "The number of F -matchings in almost every tree is a zero residue" ppt

... matchings are special cases of F -matchings. Let F and G be graphs. An F -matching in G is a subgraph o f G consisting of pairwise vertex disjoint copies of F . We say that the F -matching is ... set of F -matchings not covering v being a separate cla ss C 0 . We argue that the number of F -matchings in each such class is a zero residue...

Ngày tải lên: 08/08/2014, 12:23

... The Number of Solutions of X 2 = 0in Triangular Matrices Over GF(q) Shalosh B. EKHAD 1 and Doron ZEILBERGER 1 Abstract: We prove an explicit formula for the number of n × n upper triangular matrices, ... over GF(q), whose square is the zero matrix. This formula was recently conjectured by Sasha Kirillov and Anna Melnikov [KM]. Theorem. The number of n × n upper-triangular m...

Ngày tải lên: 07/08/2014, 06:20

... number of automorphisms of an unlabeled n-vertex graph G. The number of distinct labelings of G is n! /a( G). If f (·)isa statistic on graphs, its expectation on labeled graphs is E L (f) =  L f( G)  L 1 , where ... Gao ∗ School of Mathematics and Statistics Carleton University Ottawa K1S 5B6, Canada zgao@math.carleton.ca Nicholas C. Wormald † Department of Mathemati...

Ngày tải lên: 07/08/2014, 07:21

... permutation binomial of degree m over F q . For each other value of m, the number of monic permutation binomials of degree m over F q is the sum of N 3,m and the corresponding entry in the following table: (1) ... journal of combinatorics 13 (2006), #R65 8 The Number of Permutation Binomials Over F 4p+1 where p and 4p + 1 are Primes A. Masuda, D. Panario ∗ and Q....

Ngày tải lên: 07/08/2014, 13:21

... n. For a spanning tree A of K n , an inversion in A is a pair of vertices labelled i,j such that i > j and i is on the unique path from 1 to j in A. Let invA be the number of inversions in A. ... is originally from [1] but a proof may also be found in [7]. The fact that the value J n+1 (−1) equals a n is mentioned in [6] but a proof of this tog...

Ngày tải lên: 07/08/2014, 15:22

... number of walks ending at (n, 0) give rise to the Fibonacci numbers and if w = ∞, the Catalan numbers [St]. 3 The Main Result - Basketball Games Definition 1 An [ij] walk is a walk that starts at ... references to the number of such basketball games for various values of w. For w = 2, ··· , 6 and w = ∞, the sequence of games ending at n : n is in [Sl]. Except for the case...

Ngày tải lên: 07/08/2014, 15:22

... can use the number of planar graphs and the number of triangulations as lower bounds. Determining the number (of graphs of sub-classes) of planar graphs has attracted considerable attention [1, ... Kuratowski’s theorem [10] planar graphs are K 3,3 - and K 5 -minor- free. Hence, the class of (maximal) planar graphs is contained in the class of maximal K 3,3 -minor-free g...

Ngày tải lên: 07/08/2014, 21:20

... a triangulation. • The Auslander-Reiten translation of a diagonal from a to b is given by clockwise rotation of the diagonal if a = b. If a = b the AR-translation is g iven by clockwise rotation ... describing an explicit correspondence to a certain class of rooted trees. A tree in this class is constructed by taking a family of full binary trees T 1 , . . ....

Ngày tải lên: 07/08/2014, 21:21

... in this list of length 29. the electronic journal of combinatorics 18 (2011), #P6 7 The Number of Positions Starting a Square in Binary Words Tero Harju Department of Mathematics University of ... of Turku, Finland harju@utu.fi Tomi K¨arki Department of Mathematics University of Turku, Finland topeka@utu.fi Dirk Nowotka Institute for Formal Methods in Computer Scienc...

Ngày tải lên: 08/08/2014, 12:23

... property of downsets in regular ranked posets. A ranked poset P is regular provided that every element of rank k is comparable to the same number of elements of rank k + 1, and likewise k − 1. (Thisistherequirement that ... 1996 Abstract The weight of a vector in the finite vector space GF(q) n is the number of nonzero components it contains. We show that for a...

Ngày tải lên: 07/08/2014, 06:20