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Branden's Conjectures on the Boros-Moll Polynomials
Boros-Moll Polynomials Real-rootedness Sturm sequence, 3-log-concavity
2012/5/24
We prove two conjectures of Br\"{a}nd\'{e}n on the real-rootedness of polynomials $Q_n(x)$ and $R_n(x)$ which are related to the Boros-Moll polynomials $P_n(x)$. In fact, we show that both $Q_n(x)$ an...
Benjamini--Schramm continuity of root moments of graph polynomials
Graph polynomial of exponential type Tutte polynomial Chromatic polynomial Benjamini–Schramm convergence Sokal bound
2012/4/18
Recently, M.\ Ab\'ert and T.\ Hubai studied the following problem. The chromatic measure of a finite simple graph is defined to be the uniform distribution on its chromatic roots. Ab\'ert and Hubai pr...
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...
A catalogue of small regular matroids and their Tutte polynomials
catalogue of small regular matroids Tutte polynomials Combinatorics
2011/8/29
Abstract: A catalogue of all non-isomorphic simple connected regular matroids ${\cal M}$ of cardinality $n \leq 15$ is provided on the net. These matroids are given as binary matrix matroids and are s...
Matrix Valued Orthogonal Polynomials related to (SU(2) x SU(2),diag)
Matrix Valued Orthogonal Polynomials (SU(2) x SU(2),diag)
2011/1/21
The matrix-valued spherical functions for the pair (K × K,K), K = SU(2), are studied. By
restriction to the subgroup A the matrix-valued spherical functions are diagonal. For suitable set of represen...
Loop symmetric functions and factorizing matrix polynomials
Loop symmetric functions factorizing matrix polynomials
2011/1/18
These are notes for my talk at ICCM 2010, Beijing. We survey some results, obtained jointly with Pavlo Pylyavskyy, concerning the ring of loop symmetric functions. Motivations from networks on surface...
Minimal Polynomials of Some Matrices Via Quaternions
Minimal Polynomials Matrices Quaternions
2010/12/16
This work provides explicit characterizations and formulae for the minimal polynomials of
a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and orthogonal matrices. Ap...
Average characteristic polynomials in the two-matrix model
Two-matrix model average characteristic polynomial
2010/12/6
The two-matrix model is defined on pairs of Hermitian matrices (M1,M2) of size n × n by the probability measure 1 Zn exp (Tr(−V (M1) −W(M2) + M1M2)) dM1 dM2, where V and W are given poten...
Minimal Polynomials of Some Matrices Via Quaternions
Minimal Polynomials Matrices Quaternions
2010/12/16
This work provides explicit characterizations and formulae for the minimal polynomials of
a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and
orthogonal matrices. A...