Related papers: Another Method for Proving a Hypergeometric Genera…

We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We…

The interaction of matter with gravity in two dimensional spacetimes can be supplemented with a geometrical force analogous to a Lorentz force produced on a surface by a constant perpendicular magnetic field. In the special case of constant…

We define a new statistic on the even hyperoctahedral groups which is a natural analogue of the odd length statistic recently defined and studied on Coxeter groups of types $A$ and $B$. We compute the signed (by length) generating function…

In this paper we explore a class of equivalence relations over $\N^\ast$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of…

A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…

This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results

We construct a 2-generator recursively presented group with infinite torsion length. We also explore the construction in the context of solvable and word-hyperbolic groups.

We introduce hypergeometric-type sequences. They are linear combinations of interlaced hypergeometric sequences (of arbitrary interlacements). We prove that they form a subring of the ring of holonomic sequences. An interesting family of…

Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial…

Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…

For an oriented cohomology theory A and a relative cellular space X, we decompose the A-motive of X into a direct sum of twisted motives of the base spaces. We also obtain respective decompositions of the A-cohomology of X. Applying them,…

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.

We propose a simple definition of a Born geometry in the framework of K\"unneth geometry. While superficially different, this new definition is equivalent to the known definitions in terms of para-quaternionic or generalized geometries. We…

We define a generalization of Coxeter graphs and an associated Coxeter system and Coxeter mapping class. These can be used to construct periodic Coxeter mapping classes on surfaces with arbitrarily large genus, preserving lots of…

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…

Metric currents are, in a certain sense, a metric analogous of flat currents, therefore are related to the geometry of the space and of their support. In this short note, we try to give some evidence for the previous statement, by showing…

An afinne-invariant view of generating functions of symplectic transformations of an affine symplectic space is discussed. More generally, it works for symmetric symplectic spaces. The note is completely elementary, but it yields some nice…

In this note we study the connection between the existence of a projective reconstruction and the existence of a fundamental matrix satisfying the epipolar constraints.

In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehensive survey. The lectures include a brief explanation of…

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…