Pseudo-polynomial functions over finite distributive lattices

In this paper we consider an aggregation model f: X1 x ... x Xn --> Y for arbitrary sets X1, ..., Xn and a finite distributive lattice Y, factorizable as f(x1, ..., xn) = p(u1(x1), ..., un(xn)), where p is an n-variable lattice polynomial function over Y, and each uk is a map from Xk to Y. The resulting functions are referred to as pseudo-polynomial functions. We present an axiomatization for this class of pseudo-polynomial functions which differs from the previous ones both in flavour and nature, and develop general tools which are then used to obtain all possible such factorizations of a given pseudo-polynomial function.Comment: 16 pages, 2 figure

Proofs of some binomial identities using the method of last squares

We give combinatorial proofs for some identities involving binomial sums that have no closed form.Comment: 8 pages, 16 figure

A generalization of Goodstein's theorem: interpolation by polynomial functions of distributive lattices

We consider the problem of interpolating functions partially defined over a distributive lattice, by means of lattice polynomial functions. Goodstein's theorem solves a particular instance of this interpolation problem on a distributive lattice L with least and greatest elements 0 and 1, resp.: Given an n-ary partial function f over L, defined on all 0-1 tuples, f can be extended to a lattice polynomial function p over L if and only if f is monotone; in this case, the interpolating polynomial p is unique. We extend Goodstein's theorem to a wider class of n-ary partial functions f over a distributive lattice L, not necessarily bounded, where the domain of f is a cuboid of the form D={a1,b1}x...x{an,bn} with ai<bi, and determine the class of such partial functions which can be interpolated by lattice polynomial functions. In this wider setting, interpolating polynomials are not necessarily unique; we provide explicit descriptions of all possible lattice polynomial functions which interpolate these partial functions, when such an interpolation is available.Comment: 12 page

On categorical equivalence of finite p-rings

We prove that finite categorically equivalent p-rings have isomorphic additive groups (in particular, they have the same cardinality) and that the number of generators is a categorical invariant for finite rings. We also classify rings of size p (3) up to categorical equivalence

Associative spectra of graph algebras II: Satisfaction of bracketing identities, spectrum dichotomy

Funding Information: This work is funded by National Funds through the FCT—Fundação para a Ciência e a Tecnologia, I.P., under the scope of the Project UIDB/00297/2020 (Center for Mathematics and Applications) and the Project PTDC/MAT-PUR/31174/2017. Funding Information: Research partially supported by the Hungarian Research, Development and Innovation Office Grant K115518, and by Grant TUDFO/47138-1/2019-ITM of the Ministry for Innovation and Technology, Hungary. Publisher Copyright: © 2021, The Author(s).A necessary and sufficient condition is presented for a graph algebra to satisfy a bracketing identity. The associative spectrum of an arbitrary graph algebra is shown to be either constant or exponentially growing.publishersversionepub_ahead_of_prin