Given a finite set P ⊆ R d, called a pattern, tP (n) denotes the maximum number of translated copies of P determined by n points in R d. We give the exact value of tP (n) when P is a rational simplex, that is, the points of P are rationally affinely independent. In this case, we prove that tP (n

Given a finite set P ⊆ Rd, called a pattern, tP (n) denotes the maximum number of translated copies of P determined by n points in Rd. Wegivetheexactvalueof tP (n) when P is a rational simplex, that is, the points of P are rationally affinely independent. In this case, we prove that tP (n) =n − mr

Abstract. A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for various graph classes. For example, we prove that the maximum number of cliques in a planar graph with n vertices is 8(n − 2). 1.

bulletin board ref.: gr-qc/9409028 It is shown that N 2 is the upper limit for the number of histories in a decohering family of N-state quantum system. Simple criterion is found for a family of N 2 fine grained decohering histories of Gell-Mann and Hartle to be identical with a family of Griffiths

Through handson exploration, participants will discover different types of animal signs that are used to learn about and track animals big and small.

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Using Razborov’s flag algebras we show that a triangle-free graph on n vertices contains at most n

The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/.

Abstract. Let A be an m×n, (0, 1)-matrix. A submatrix of A is odd if the sum of its entries is an odd integer and even otherwise. The maximum number of 2×2 odd submatrices in a (0, 1)-matrix is related to the existence of Hadamard matrices and bounds on Turán numbers. Pinelis [On the minimal

The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximumlikelihood principle, which clearly satisfies these requirements