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Determination of Integral Cayley Graphs on Finite Abelian Groups
abelian group character cayley graph integral graph
2012/6/21
A graph is integral means that all its eigenvalues are integers. In this note, we determine all the integral Cayley graphs on finite abelian groups. Moreover, we calculate the the number of integral C...
Ehrhart polynomials of integral simplices with prime volumes
Integral simplex Ehrhart polynomial δ-vector
2011/9/20
Abstract: For an integral convex polytope $\Pc \subset \RR^N$ of dimension $d$, we call $\delta(\Pc)=(\delta_0, \delta_1,..., \delta_d)$ its $\delta$-vector and $\vol(\Pc)=\sum_{i=0}^d\delta_i$ its no...
Monotone Hurwitz numbers and the HCIZ integral II
Hurwitz numbers matrix models enumerative geometry Combinatorics
2011/8/25
Abstract: Motivated by results for the HCIZ integral in Part I of this paper, we study the structure of monotone Hurwitz numbers, which are a desymmetrized version of classical Hurwitz numbers. We pro...