G'abor Cz'edli

activity

20122021

most citedCoordinatization of join-distributive lattices

20 citations · 41 across the 14 of their papers we have counts for

collaborators

33 papers

math.RA2021

Length-preserving extensions of semimodular lattices by lowering join-irreducible elements

Gábor Czédli

We prove that if $e$ is a join-irreducible element of a semimodular lattice $L$ of finite length and $h < e$ in $L$ such that $e$ does not cover $h$ , then $e$ can be "lowered" to a c…

math.CO2021

Revisiting Faigle geometries from a perspective of semimodular lattices

Gábor Czédli

In 1980, U. Faigle introduced a sort of finite geometries on posets that are in bijective correspondence with finite semimodular lattices. His result has almost been forgotten in l…

math.RA2021

Absolute retracts for finite distributive lattices and slim semimodular lattices

Gábor Czédli, Ali Molkhasi

We describe the absolute retracts for the following classes of finite lattices: (1) slim semimodular lattices, (2) finite distributive lattices, and for each positive integer $n$ ,…

math.RA2021★ 3 cited

Slim patch lattices as absolute retracts and maximal lattices

Gábor Czédli

Patch lattices, introduced by G. Czédli and E.T. Schmidt in 2013, are the building stones for slim (and so necessarily finite and planar) semimodular lattices with respect to gluin…

math.CO2021

(1+1+2)-generated lattices of quasiorders

Delbrin Ahmed, Gábor Czédli

A lattice is $(1 + 1 + 2)$ -generated if it has a four-element generating set such that exactly two of the four generators are comparable. We prove that the lattice Quo $(n)$ of all quas…

math.LO2021

Cyclic congruences of slim semimodular lattices and non-finite axiomatizability of some finite structures

Gábor Czédli

We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among FINITE graphs. (This fact is a consequence of a gene…

math.RA2021

Lamps in slim rectangular planar semimodular lattices

Gábor Czédli

A planar (upper) semimodular lattice $L$ is slim if the five-element nondistributive modular lattice $M_{3}$ does not occur among its sublattices. (Planar lattices are finite by defi…

math.RA2020

Atoms and coatoms in three-generated lattices

Gábor Czédli

In addition to the unique cover $M^{+}$ of the variety of modular lattices, we also deal with those twenty-three known covers of $M^{+}$ that can be extracted from the literature. For…

math.CO2020

Four-element generating sets of partition lattices and their direct products

Gábor Czédli, Lillian Oluoch

Let $n > 3$ be a natural number. By a 1975 result of H. Strietz, the lattice Part $(n)$ of all partitions of an $n$ -element set has a four-element generating set. In 1983, L. Zádori g…

math.RA2020

Four-generated direct powers of partition lattices and authentication

Gábor Czédli

For an integer $n \geq 5$ , H. Strietz (1975) and L. Zádori (1986) proved that the lattice Part $(n)$ of all partitions of ${1, 2, \dots, n}$ is four-generated. Developing L. Zádori's…

math.RA2020

On the number of atoms in three-generated lattices

Gábor Czédli

As the main achievement of the paper, we construct a three-generated, 2-distributive, atomless lattice that is not finitely presented. Also, the paper contains the following three…

math.RA2019

Medians are below joins in semimodular lattices of breadth 2

Gábor Czédli, Robert C. Powers, Jeremy M. White

Let $L$ be a lattice of finite length and let $d$ denote the minimum path length metric on the covering graph of $L$ . For any $ξ = (x_{1}, \dots, x_{k}) \in L^{k}$ , an element $y$ belonging t…

math.RA2019

Permuting 2-uniform tolerances on lattices

Gábor Czédli

A $2$ -uniform tolerance on a lattice is a compatible tolerance relation such that all of its blocks are 2-element. We characterize permuting pairs of 2-uniform tolerances on lattic…

math.RA2019★ 1 cited

Doubling tolerances and coalition lattices

Gábor Czédli

If every block of a (compatible) tolerance (relation) $T$ on a modular lattice $L$ of finite length consists of at most two elements, then we call $T$ a \emph{doubling tolerance} o…

math.RA2019

Planar semilattices and nearlattices with eighty-three subnearlattices

Gábor Czédli

Finite (upper) nearlattices are essentially the same mathematical entities as finite semilattices, finite commutative idempotent semigroups, finite join-enriched meet semilattices,…

math.RA2019

One hundred twenty-seven subsemilattices and planarity

Gábor Czédli

Let $L$ be a finite $n$ -element semilattice. We prove that if $L$ has at least $127 \cdot 2^{n - 8}$ subsemilattices, then $L$ is planar. For $n > 8$ , this result is sharp since there i…

math.RA2019

Eighty-three sublattices and planarity

Gábor Czédli

Let $L$ be a finite $n$ -element lattice. We prove that if $L$ has at least $83 \cdot 2^{n - 8}$ sublattices, then $L$ is planar. For $n > 8$ , this result is sharp since there is a non-p…

math.RA2018

A note on lattices with many sublattices

Gábor Czédli, Eszter K. Horváth

For every natural number $n \geq 5$ , we prove that the number of subuniverses of an $n$ -element lattice is $2^{n}$ , $13 \cdot 2^{n - 4}$ , $23 \cdot 2^{n - 5}$ , or less than $23\cdot 2^{n-5}…

math.MG2018

A convex combinatorial property of compact sets in the plane and its roots in lattice theory

Gábor Czédli, Árpád Kurusa

K. Adaricheva and M. Bolat have recently proved that if $U_{0}$ and $U_{1}$ are circles in a triangle with vertices $A_{0}, A_{1}, A_{2}$ , then there exist $j \in {0, 1, 2}$ and $k \in {0, 1}$ s…

math.RA2017★ 14 cited

A note on finite lattices with many congruences

Gábor Czédli

By a twenty year old result of Ralph Freese, an $n$ -element lattice $L$ has at most $2^{n - 1}$ congruences. We prove that if $L$ has less than $2^{n - 1}$ congruences, then it has at…

math.RA2017

On principal congruences and the number of congruences of a lattice with more ideals than filters

Gábor Czédli, Claudia Mureşan

Let $λ$ and $κ$ be cardinal numbers such that $κ$ is infinite and either $2 \leq λ \leq κ$ , or $λ = 2^{κ}$ . We prove that there exists a lattice $L$ with exactly $λ$ many congruences, $2…

math.RA2017

On the set of principal congruences in a distributive congruence lattice of an algebra

Gábor Czédli

Let $Q$ be a subset of a finite distributive lattice $D$ . An algebra $A$ represents the inclusion $Q \subseteq D$ by principal congruences if the congruence lattice of $A$ is isomor…

math.CO2016★ 3 cited

A note and a short survey on supporting lines of compact convex sets in the plane

Gábor Czédli, László L. Stachó

After surveying some known properties of compact convex sets in the plane, we give a two rigorous proofs of the general feeling that supporting lines can be slide-turned slowly and…

math.MG2016

Characterizing circles by a convex combinatorial property

Gábor Czédli

Let $K_{0}$ be a compact convex subset of the plane $R^{2}$ , and assume that $K_{1} \subseteq R^{2}$ is similar to $K_{0}$ , that is, $K_{1}$ is the image of $K_{0}$ with respect t…