G. Czédli

activity

20122022

most citedNotes on planar semimodular lattices. VII. Resections of planar semimodular lattices

26 citations · 86 across the 20 of their papers we have counts for

collaborators

26 papers

math.RA2022

Lattice tolerances and congruences

Gábor Czédli, George Grätzer

We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.

math.RA2022

Congruence structure of planar semimodular lattices: The General Swing Lemma

Gábor Czédli, George Grätzer, Harry Lakser

The Swing Lemma of the second author describes how a congruence spreads from a prime interval to another in a slim (having no $M_{3}$ sublattice), planar, semimodular lattice. We gen…

math.RA2018

Lattices with many congruences are planar

Gábor Czédli

Let $L$ be an $n$ -element finite lattice. We prove that if $L$ has strictly more than $2^{n - 5}$ congruences, then $L$ is planar. This result is sharp, since for each natural number…

math.RA2018

Symmetric embeddings of free lattices into each other

Gábor Czédli, Gergő Gyenizse, Ádám Kunos

By a 1941 result of Ph. M. Whitman, the free lattice FL(3) on three generators includes a sublattice $S$ that is isomorphic to the lattice FL( $ω$ )=FL( $ℵ_{0}$ ) generated freely b…

math.MG2018

Circles and crossing planar compact convex sets

Gábor Czédli

Let $K_{0}$ be a compact convex subset of the plane $R^{2}$ , and assume that whenever $K_{1} \subseteq R^{2}$ is congruent to $K_{0}$ , then $K_{0}$ and $K_{1}$ are not crossing in…

math.RA2018

Finite semilattices with many congruences

Gábor Czédli

For an integer $n \geq 2$ , let NCSL $(n)$ denote the set of sizes of congruence lattices of $n$ -element semilattices. We find the four largest numbers belonging to NCSL $(n)$ , provide…

math.AG2017

Geometric constructibility of polygons lying on a circular arc

Delbrin Ahmed, Gábor Czédli, Eszter K. Horváth

For a positive integer $n$ , an $n$ -sided polygon lying on a circular arc or, shortly, an $n$ -fan is a sequence of $n + 1$ points on a circle going counterclockwise such that the "tot…

math.RA2017

Characterizing fully principal congruence representable distributive lattices

Gábor Czédli

Motivated by a recent paper of G. Grätzer, a finite distributive lattice $D$ is said to be fully principal congruence representable if for every subset $Q$ of $D$ containing $0$ , $…

math.CO2016

Permutation groups, pattern involvement, and Galois connections

Erkko Lehtonen, Reinhard Pöschel

There is a connection between permutation groups and permutation patterns: for any subgroup $G$ of the symmetric group $S_{ℓ}$ and for any $n \geq ℓ$ , the set of $n$ -permutatio…

math.CT2015

Cometic functors for small concrete categories and an application

Gabor Czedli

Our goal is to derive some families of maps, also known as functions, from injective maps and surjective maps; this can be useful in various fields of mathematics. Let A be a small…

math.RA2014

Diagrams and rectangular extensions of planar semimodular lattices

Gábor Czédli

In 2009, G. Grätzer and E. Knapp proved that every planar semimodular lattice has a rectangular extension. We prove that, under reasonable additional conditions, this extension is…

math.RA2014

Representing some families of monotone maps by principal lattice congruences

Gábor Czédli

For a lattice L with 0 and 1, let Princ L denote the ordered set of principal congruences of L. For {0,1}-sublattices A subseteq B of L, congruence generation defines a natural map…

math.RA2013

CD-independent subsets in meet-distributive lattices

Gabor Czedli

A subset $X$ of a finite lattice $L$ is CD-independent if the meet of any two incomparable elements of $X$ equals 0. In 2009, Czédli, Hartmann and Schmidt proved that any two maxim…

math.RA2013

The ordered set of principal congruences of a countable lattice

Gabor Czedli

For a lattice L, let Princ L denote the ordered set of principal congruences of L. In a pioneering paper, G. Gratzer characterized the ordered sets Princ L of finite lattices L; he…

math.RA2012

Quasiplanar diagrams and slim semimodular lattices

Gábor Czédli

A (Hasse) diagram of a finite partially ordered set (poset) P will be called quasiplanar if for any two incomparable elements u and v, either v is on the left of all maximal chains…

math.RA2012

Finite convex geometries of circles

Gábor Czédli

Let F be a finite set of circles in the plane. We point out that the usual convex closure restricted to F yields a convex geometry, that is, a combinatorial structure introduced by…

math.RA2012

Distributive lattices determined by weighted double skeletons

Gábor Czédli, Joanna Grygiel, Katarzyna Grygiel

Related to his S-glued sum construction, the skeleton S(L) of a finite lattice L was introduced by C. Herrmann in 1973. Our theorem asserts that if D is a finite distributive latti…

math.RA2012★ 24 cited

Notes on the description of join-distributive lattices by permutations

Gábor Czédli, Kira Adaricheva

Let L be a join-distributive lattice with length n and width(Ji L) \leq k. There are two ways to describe L by k-1 permutations acting on an n-element set: a combinatorial way give…

math.RA2012

Varieties of distributive rotational lattices

Gábor Czédli, Ildikó V. Nagy

A rotational lattice is a structure (L;\vee,\wedge, g) where L=(L;\vee,\wedge) is a lattice and g is a lattice automorphism of finite order. We describe the subdirectly irreducible…

math.RA2012

Composition series in groups and the structure of slim semimodular lattices

Gabor Czedli, E. Tamas Schmidt

Let H and K be finite composition series of a group G. The intersections H_i\cap K_j of their members form a lattice CSL(H,\K) under set inclusion. Improving the Jordan-Hölder theo…

math.RA2012★ 8 cited

Tolerances as images of congruences in varieties defined by linear identities

Ivan Chajda, Gábor Czédli, Radomir Halas +1

An identity s=t is linear if each variable occurs at most once in each of the terms s and t. Let T be a tolerance relation of an algebra A in a variety defined by a set of linear i…

math.RA2012★ 11 cited

Independent joins of tolerance factorable varieties

Ivan Chajda, Gábor Czédli, Radomir Halas

Let L denote the variety of lattices. In 1982, the second author proved that L is strongly tolerance factorable, that is, the members of L have quotients in L modulo tolerances, al…

math.RA2012★ 26 cited

Notes on planar semimodular lattices. VII. Resections of planar semimodular lattices

Gábor Czédli, George Grätzer

A recent result of G. Czédli and E.\,T. Schmidt gives a construction of slim (planar) semimodular lattices from planar distributive lattices by adding elements, adding "forks". We…

math.RA2012★ 12 cited

The asymptotic number of planar, slim, semimodular lattice diagrams

Gábor Czédli

A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. We prove that there exists a positive constant C such that, up…