Related papers: Distributive laws in residuated binars
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a finite language is congruence meet-semidistributive and residually less than some finite cardinal, then…
We prove that the universal theory and the quasi-equational theory of bounded residuated distributive lattice-orderegroupoids are both EXPTIME-complete. Similar results areproven for bounded distributive lattices with a unary or binary…
In this paper we introduce and study a variety of algebras that properly includes integral distributive commutative residuated lattices and weak Heyting algebras. Our main goal is to give a characterization of the principal congruences in…
Let $(P,\cdot,d)$ be a differential perm algebra over a field of characteristic $0$, i.e. an associative algebra satisfying $(ab)c=(ba)c$ equipped with a derivation $d$. We investigate polynomial identities in the algebras obtained from $d$…
The sets of all neutral, distributive and lower-modular elements of the lattice of semigroup varieties are finite, countably infinite and uncountably infinite, respectively. In 2018, we established that there are precisely three neutral…
We checked each binary relation on a 5-element set for a given set of properties, including usual ones like asymmetry and less known ones like Euclideanness. Using a poor man's Quine-McCluskey algorithm, we computed prime implicants of…
Given a set C of binary n-tuples and c in C, how many bits of c suffice to distinguish it from the other elements in C? We shed new light on this old combinatorial problem and improve on previously known bounds.
All known structural extensions of the substructural logic $\mathsf{FL_e}$, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$-equations)…
This note reformulates certain classical combinatorial duality theorems in the context of order lattices. For source-target networks, we generalize bottleneck path-cut and flow-cut duality results to edges with capacities in a distributive…
We propose a new approach to extending the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on ternary associativity of the first and second kind. We propose a ternary commutator,…
We consider discrete probability laws on the real line, whose characteristic functions are separated from zero. In particular, this class includes arbitrary discrete infinitely divisible laws and lattice probability laws, whose…
Let the finite distributive lattice $D$ be isomorphic to the congruence lattice of a finite lattice $L$. Let $Q$ denote those elements of $D$ that correspond to principal congruences under this isomorphism. Then $Q$ contains $0,1 \in D$ and…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
We extend the concepts of the associator and commutator from algebras with a binary multiplication law to algebras with a ternary multiplication law using cube roots of unity. By analogy with the Jacobi identity for the binary commutator,…
In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code.…
This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality are employed to give, economically and in a uniform way, categories ofstructures dually…
The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming…
We classify 8-divisible binary linear codes with minimum distance 24 and small length. As an application we consider the codes associated to nodal sextics with 65 ordinary double points.
An executable binary typically contains a large number of machine instructions. Although the statistics of popular instructions is well known, the distribution of non-popular instructions has been relatively under explored. Our finding…