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EJC
2007
13 years 11 months ago
Binary codes from rectangular lattice graphs and permutation decoding
We examine the binary codes obtained from the row span over the field F2 of an adjacency matrix of the rectangular lattice graphs L2(m, n) for 3 ≤ m < n and show that permut...
Jennifer D. Key, P. Seneviratne
EJC
2007
13 years 11 months ago
Permutation statistics on involutions
We consider in this work the enumeration of involutions by descent sets, and based on that, by descent numbers. Formulas of the number of involutions with a prescribed descent set...
W. M. B. Dukes
EJC
2007
13 years 11 months ago
Complexity of cutting words on regular tilings
: We show that the complexity of a cutting word u in a regular tiling by a polyomino Q is equal to Pn(u) = (p+q−1)n+1 for all n ≥ 0, where Pn(u) counts the number of distinct f...
Pascal Hubert, Laurent Vuillon
EJC
2007
13 years 11 months ago
On the number of Tverberg partitions in the prime power case
We give an extension of the lower bound of [9] for the number of Tverberg partitions from the prime to the prime power case. Our proof is inspired by the Zp-index version of the p...
Stephan Hell
EJC
2006
13 years 11 months ago
Product representations of polynomials
For a fixed polyomial f Z[X], let k(N) denote the maximum size of a set A {1, 2, . . . , N} such that no product of k distinct elements of A is in the value set of f. In this pap...
Jacques Verstraëte
EJC
2006
13 years 11 months ago
Matroid tree-width
Abstract. We show that the tree-width of a graph can be defined without reference to graph vertices, and hence the notion of tree-width can be naturally extended to matroids. (This...
Petr Hlinený, Geoff Whittle
EJC
2006
13 years 11 months ago
Perfect matchings in uniform hypergraphs with large minimum degree
A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. In this paper we give a sufficient condition for the existence of a p...
Vojtech Rödl, Andrzej Rucinski, Endre Szemer&...