Related papers: Matrix integrals and generating functions for perm…
We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have…
We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, continuous…
Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on…
We consider tilings of a rectangle which is n units wide and m units long by non-overlapping 1 X 1 squares and s X s squares. Bivariate generating functions are computed with the Transfer Matrix Method for moderately large but fixed widths…
We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can…
Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…
Tensors play a pivotal role in the realms of science and engineering, particularly in the realms of data analysis, machine learning, and computational mathematics. The process of unfolding a tensor into matrices, commonly known as tensor…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in the paper ``Integrals of Rational Symmetric Functions,…
We present a new tree-level matrix element generator, based on the colour dressed Berends-Giele recursive relations. We discuss two new algorithms for phase space integration, dedicated to be used with large multiplicities and colour…
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…
We study graph parameters whose associated edge-connection matrices have exponentially bounded rank growth. Our main result is an explicit construction of a large class of graph parameters with this property that we call mixed partition…
Using unfolded top-quark decay data we can measure the top quark mass, as well as search for unexpected kinematic effects. We present a new generative unfolding method for the two tasks and show how they both benefit from unbinned,…
We consider two different genus expansions of the free energy functions of Hermitian one-matrix models, one using fat graphs, one using ordinary graphs (thin graphs). Some structural results are first proved for the thin version of genus…
For loop integrals, the reduction is the standard method. Having an efficient way to find reduction coefficients is an important topic in scattering amplitudes. In this paper, we present the generation functions of reduction coefficients…
Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…
Bipolar orientations of planar maps have recently attracted some interest in combinatorics, probability theory and theoretical physics. Plane bipolar orientations with $n$ edges are known to be counted by the $n$th Baxter number $b(n)$,…