Related papers: Intersection matrices revisited
It is shown that the new Poisson brackets proposed in Part I of this work (J. Math. Phys. 34, 5747(hep-th/9305133)) arise naturally in an extension of the formal variational calculus incorporating divergences. The linear spaces of local…
We exhibit explicit expressions, in terms of components, of discriminants, determinants, characteristic polynomials and polynomial identities for matrices of higher rank. We define permutation tensors and in term of them we construct…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
Inspired by earlier works on representations of the Temperley-Lieb algebra we introduce a novel family of representations of the algebra. This may be seen as a generalization of the so called asymmetric twin representation. The underlying…
We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two elementary blocks it is possible to represent these relations in a…
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing…
We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence $a_{i,j}=a_{i-1,j}+a_{i,j-1}$, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland…
Given two curves in $\PP^3$, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the…
The aim of this article is to provide a complementary understanding to some results of the second author using the machinery of Koszul complexes, and to explain how this approach can provide a new description of projective derived…
We study the structure of the Goulden-Jackson-Vakil formula that relates Hurwitz numbers to some conjectural "intersection numbers" on a conjectural family of varieties $X_{g,n}$ of dimension $4g-3+n$. We give explicit formulas for the…
Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or -1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We present a unifying perspective on ASMs and other combinatorial objects by studying…
We give some interpretations to certain integer sequences in terms of parameters on Grand-Dyck paths and coloured noncrossing partitions, and we find some new bijections relating Grand-Dyck paths and signed pattern avoiding permutations.…
We study the generalized supersymmetric t-J model with Kondo impurities in the boundaries. We first construct the higher spin operator K-matrix for the XXZ Heisenberg chain. Setting the boundary parameter to be a special value, we find a…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…
The decomposition into interaction subspaces is a hierarchical decomposition of the spaces of cylindrical functions of a finite product space, also called factor spaces. It is an important construction in graphical models and a standard way…
We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics. The three main types of problems we…
We investigate arcs on a pair of pants and present an algorithm to compute the self-intersection number of an arc. Additionally, we establish bounds for the self-intersection number in terms of the word length. We also prove that the…
In the theory of line graphs of undirected graphs there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, the exists no analogous…
The problems connected with Gaudin models are reviewed by analyzing model related to the trigonometric osp(1|2) classical r-matrix. The eigenvectors of the trigonometric osp(1|2) Gaudin Hamiltonians are found using explicitly constructed…