Related papers: Un invariant remarquable des polytopes simples

An invariant of a model of genus one curve is a polynomial in the coefficients of the model that is stable under certain linear transformations. The classical example of an invariant is the discriminant, which characterizes the singularity…

We present a generalization of Descartes' theorem for the family of polytopal sphere packings arising from uniform polytopes. The corresponding quadratic equation is expressed in terms of geometric invariants of uniform polytopes which are…

We study $n$-vertex $d$-dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called {\it almost simplicial polytopes}. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$…

Probably we have observed a new simple phenomena dealing with approximations to two real numbers.

Given a finite simplicial complex L and a collection of pairs of spaces indexed by its vertex set, one can define their polyhedral product. We record a simple formula for its Euler characteristic. In special cases the formula simplifies…

All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…

We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…

Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring…

A very simple but useful almost sure convergence theorem of probability is given.

We generalize the notion of the quandle polynomial to the case of singquandles. We show that the singquandle polynomial is an invariant of finite singquandles. We also construct a singular link invariant from the singquandle polynomial and…

In this paper, we use a simple discrete dynamical model to study partitions of integers into powers of another integer. We extend and generalize some known results about their enumeration and counting, and we give new structural results. In…

We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…

We are presenting an algorithm capable of simplifying tensor polynomials with indices when the building tensors have index symmetry properties. These properties include simple symmetry, cyclicity and those due to the presence of partial and…

Cutting a polytope is a very natural way to produce new classes of interesting polytopes. Moreover, it has been very enlightening to explore which algebraic and combinatorial properties of the orignial polytope are hereditary to its…

We classify here combinatorially rigid simple polytopes with three facets more than their dimension.

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.

We classify general systems of polynomial equations with a single solution, or, equivalently, collections of lattice polytopes of minimal positive mixed volume. As a byproduct, this classification provides an algorithm to evaluate the…

We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability…

Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.

We consider invariants of a finite group related to the number of random (independent, uniformly distributed) conjugacy classes which are required to generate it. These invariants are intuitively related to problems of Galois theory. We…