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COMBINATORICS
2007
15 years 3 months ago
2007
The density matrix of a graph is the combinatorial laplacian matrix of a graph normalized to have unit trace. In this paper we generalize the entanglement properties of mixed dens...
112
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COMBINATORICS
2007
15 years 3 months ago
2007
The known bijections on Dyck paths are either involutions or have notoriously intractable cycle structure. Here we present a size-preserving bijection on Dyck paths whose cycle st...
133
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COMBINATORICS
2007
15 years 3 months ago
2007
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) Let G be a regular graph of order n and finite di...
122
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COMBINATORICS
2007
15 years 3 months ago
2007
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) If H is a proper subgraph of a connected graph G o...
116
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COMBINATORICS
2007
15 years 3 months ago
2007
Let k3(n) denote the minimal cardinality of a ternary code of length n and covering radius one. In this paper we show k3(7) ≥ 156 and k3(8) ≥ 402 improving on the best previou...