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COMBINATORICS
1998
14 years 9 months ago
1998
We show that the moments of the trace of a random unitary matrix have combinatorial interpretations in terms of longest increasing subsequences of permutations. To be precise, we s...
COMBINATORICS
1999
14 years 9 months ago
1999
An asymptotic estimate is given for the coefficients of products of large powers of generating functions. This theorem and another local limit theorem which is useful for conditio...
COMBINATORICS
1999
14 years 9 months ago
1999
Let Pn and Qn be the polynomials obtained by repeated differentiation of the tangent and secant functions respectively. From the exponential generating functions of these polynomia...
COMBINATORICS
2007
14 years 9 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...
COMBINATORICS
2006
14 years 9 months ago
2006
A set of vertices S is a determining set for a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of a graph is the size of a sma...