Related papers: On mappings of terms determined by hypersubstituti…
This work presents a generalized notion of multiset mapping thus resolving a long standing obstacle in structural study of multiset processing. It has been shown that the mapping defined herein can model a vast array of notions as special…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The category of all monads over many-sorted sets (and over other "set-like" categories) is proved to have coequalizers and strong cointersections. And a general diagram has a colimit whenever all the monads involved preserve monomorphisms…
In this paper, we characterize the monoid of endomorphisms of the semigroup of all monotone full transformations of a finite chain, as well as the monoids of endomorphisms of the semigroup of all monotone partial transformations and of the…
We give a characterization of a matroid to be paving, through its set of hyperplanes and give an algorithm to construct all of them.
We establish extension theorems for separately holomorphic mappings defined on sets of the form W\setminus M with values in a complex analytic space which possesses the Hartogs extension property. Here W is a 2-fold cross of arbitrary…
The hyperdeterminant of a polynomial (interpreted as a symmetric tensor) factors into several irreducible factors with multiplicities. Using geometric techniques these factors are identified along with their degrees and their…
We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to characterize posets in which some of these mappings coincide. We define special mappings determined…
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including Whitney polynomials, characteristic polynomials, Whitney…
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
We show that every source connected Lie groupoid always has global bisections through any given point. This bisection can be chosen to be the multiplication of some exponentials as close as possible to a prescribed curve. The existence of…
The Hadamard Extension of a matrix is the matrix consisting of all Hadamard products of subsets of its rows. This construction arises in the context of identifying a mixture of product distributions on binary random variables: full column…
We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity…
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
We consider the complexities of substitutive sequences over a binary alphabet. By studying various types of special words, we show that, knowing some initial values, its complexity can be completely formulated via a recurrence formula…
We continue investigating the structure of externally definable sets in NIP theories and preservation of NIP after expanding by new predicates. Most importantly: types over finite sets are uniformly definable; over a model, a family of…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.