Related papers: The Profile of relations
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…
Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an efficient design of the related algorithm have been solidly…
Piecewise quasipolynomial growth of Presburger counting functions combines with tame persistent homology module theory to conclude piecewise quasipolynomial behavior of constructible families of finely graded modules over constructible…
We study the Hilbert function and the graded Betti numbers of almost complete intersection artinian algebras. We show that that every Hilbert function of a complete intersection artinian algebra is the Hilbert function of an almost complete…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
The coefficient of x^{-1} of a formal Laurent series f(x) is called the formal residue of f(x). Many combinatorial numbers can be represented by the formal residues of hypergeometric terms. With these representations and the extended…
The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown whether toric Hilbert schemes are connected. We construct a…
In general terms, we establish algebraic relations that numbers must satisfy in order for their images to match after one or several transformations. Some groups associated with these relationships are identified, such as the Klein group.…
We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by n generators and n(n-1)/2 relations…
A relational structure $\mathbb{X}$ is called reversible iff each bijective homomorphism from $\mathbb{X}$ onto $\mathbb{X}$ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible…
For an arbitrary group, the subgroups form a lattice with order determined by set inclusion. Not every lattice is isomorphic to the subgroup lattice for a group. However, Birkhoff and Frink proved that any compactly generated lattice is…
It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component.…
In the present paper we propose a new approach on `distributed systems': the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations…
We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for…
For a standard graded algebra $R$, we consider embeddings of the the poset of Hilbert functions of quotients of $R$ into the poset of ideals of $R$, as a way of classification of Hilbert functions. There are examples of rings for which such…
We give a new proof for a theorem of Ehrhart regarding the quasi-polynomiality of the function that counts the number of integer points in the integral dilates of a rational polytope. The proof involves a geometric bijection,…
Let $n$ be a positive integer and let $A$ be nonempty finite set of positive integers. We say that $A$ is relatively prime if $\gcd(A) =1$ and that $A$ is relatively prime to $n$ if $\gcd(A,n)=1$. In this work we count the number of…
The organizational structure of a network is investigated with a simulated precipitation model which does not make use of prior knowledge about the community structure of the network. The result is presented as a structure profile through…
Given a hereditary class $\mathcal{F}$ of finite relational structures, the rank function $\mathsf{rk}:\sigma\mathcal{F}\to\omega_1\cup\{\infty\}$, introduced by Kubi\'{s} and Shelah, measures how far a countable structure is from being…