Báo cáo toán học: "A Discontinuity in the Distribution of Fixed Point Sums" pps

... See http://mathworld.wolfram.com/BernsteinPolynomial.html the electronic journal of combinatorics 10 (2003), #R15 17 A Discontinuity in the Distribution of Fixed Point Sums Edward A. Bender Department of Mathematics University of ... n} whose fixed points sum to r, shows a sharp discontinuity in the neigh- borhood of r = n. We explain this discontinuity and stud...

Ngày tải lên: 07/08/2014, 07:21

... is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t,k (v) be the (0,1)-matrix of inclusions for t-subsets ... inclusions for t-subsets versus k-subsets of X : W T,K =1ifT is contained in K, and 0 otherwise. These matrices play a significant part in several combinatorial investigation...

Ngày tải lên: 07/08/2014, 06:22

... to a circle C (not necessarily injective). 2. There is a set of intervals I of C, none including another, such that no point of C is an endpoint of more than one interval so tha t: (a) If two ... called a linear interval strip if G is a linear interval graph with vertices v 1 , . . . , v n listed in the order of their appearances in the linear interval representation of...

Ngày tải lên: 08/08/2014, 14:23

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Ngày tải lên: 05/08/2014, 15:20

... specifying conditions on the cardinality of the edge-set of the digraph that guarantee the existence of a directed simple cycle of length at most four. As usual in Tur´an type problems in directed ... done. the electronic journal of combinatorics 9 (2001), #N6 2 giving inequality (a). To prove inequality (b), let M  be the submatrix of M consisting of rows βm+1,...

Ngày tải lên: 07/08/2014, 06:23

... repeat the above argument with the portion of R  beginning at u m−1 and the vertex u m . Theorem 1. Let h p (n) be the minimum number of distinct hamiltonian paths in a strong tournament of order ... u j on R. Proof. Note that we allow the special case where m = 0; in this case the path Q is a path on 0 vertices, and R = P satisfies the lemma trivially. The remainder...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 15:21

... Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the electronic journal of combinatorics 7 (2000), #R30 7 Proof. We need to show that the left-hand side of (4) is ... Combinatorica 18 (1998), 449– 459. [3]N.J.Calkin,On the number of sum-free sets, Bull. Lond. Math. Soc. 22 (1990), 141–144. [4] N. J. Calkin, A. C. Taylor: Counting sets...

Ngày tải lên: 07/08/2014, 06:20

... constraint in the structure of trees or indeed all higher plants. If we seek meaning in the list as a whole there remains the task of “seeing the wood for the trees”, selecting and arranging them into ... contain them. On the other hand, each could be examined for indications of non-viability. 4.2 Gradients But the intended purpose of the rules was to aid the di...

Ngày tải lên: 08/08/2014, 14:22