arXiv subjects

Miklós Maróti

Publications and source records attributed to Miklós Maróti.

7 recordsLinked to original sources

arXiv2026

The filter of interpretability types of Hobby-McKenzie varieties is prime

We study the Hobby-McKenzie varieties that constitute a major class investigated thoroughly in the monograph The shape of congruence lattices by Kearnes and Kiss. We obtain new characterizations of the Hobby-McKenzie varieties via compatible reflexive ternary structures. Based on our findings, we prove that in the lattice of interpretability types of varieties, the filter of the interpretability types of Hobby-McKenzie varieties is prime.

math.CO↗

arXiv2026

SMB algebras II: On the Constraint Satisfaction Problem over Semilattices of Mal'cev Blocks

We define a class of algebras, the semilattices of Mal'cev blocks (for short, SMB algebras). In a nutshell, these algebras are semilattices in which each element gets blown up into a Mal'cev algebra. We publish for the first time our old proofs that some SMB algebras induce tractable templates of the reprove that the Constraint Satisfaction Problem. Next, we reprove that, in fact, all SMB algebras induce tractable templates of the Constraint Satisfaction Problem, a result already proved by A. Bulatov. Also, we compare the two general proofs of the CSP Dichotomy and prove they are more similar than initially thought when they are applied to SMB algebras. This paper is the second in the series of papers investigating the SMB algebras and it is a precursor to our further research on the similarities between the proofs of the Dichotomy Theorem.

cs.CC↗

arXiv2026

Connectivity notions on compatible digraphs in equational classes

A digraph $\mathbb G$ is called weakly connected, strongly connected, and extremely connected if any two vertices of $\mathbb G$ are connected respectively by an oriented, a directed, and a symmetric path in $\mathbb G$. We investigate the algebraic properties of digraphs that force some of these connectivity notions to coincide. We prove that for digraphs with a Hobby-McKenzie polymorphism, the strong and the extreme components coincide. Conversely, if the strong and the extreme components of any compatible digraph in an equational class of algebras coincide, then the class must have a Hobby-McKenzie term. As a consequence, we obtain that an equational class $\mathcal V$ is $n$-permutable for some $n$ if and only if the weak components of any compatible reflexive digraph in $\mathcal V$ are extremely connected.

math.CO↗

arXiv2024

Taylor is prime

We study the Taylor varieties and obtain new characterizations of them via compatible reflexive digraphs. Based on our findings, we prove that in the lattice of interpretability types of varieties, the filter of the types of all Taylor varieties is prime.

math.CO↗

arXiv2021

Congruence permutability is prime

We give a combinatorial proof that congruence permutability is prime in the lattice of interpretability types of varieties. Thereby, we settle a 1984 conjecture of Garcia and Taylor.

math.CO↗

arXiv2012

A dyadic view of rational convex sets

Let F be a subfield of the field R of real numbers. Equipped with the binary arithmetic mean operation, each convex subset C of F^n becomes a commutative binary mode, also called idempotent commutative medial (or entropic) groupoid. Let C and C' be convex subsets of F^n. Assume that they are of the same dimension and at least one of them is bounded, or F is the field of all rational numbers. We prove that the corresponding idempotent commutative medial groupoids are isomorphic iff the affine space F^n over F has an automorphism that maps C onto C'. We also prove a more general statement for the case when C,C'\subseteq F^n are considered barycentric algebras over a unital subring of F that is distinct from the ring of integers. A related result, for a subring of R instead of a subfield F, is given in \cite{rczgaroman2}.

math.RA↗

arXiv2007

CD(4) has bounded width

We prove that the constraint languages invariant under a short sequence of Jónsson terms (containing at most three non-trivial ternary terms) are tractable by showing that they have bounded width. This improves the previous result by Kiss and Valeriote and presents some evidence that the Larose-Zadori conjecture holds in the congruence-distributive case.

math.LO↗