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of 202
pro vyhledávání: '"06C10"'
Double circuits were introduced by Lov\'{a}sz in 1980 as a fundamental tool in his derivation of a min-max formula for the size of a maximum matching in certain families of matroids. This formula was extended to all matroids satisfying the so-called
Externí odkaz:
http://arxiv.org/abs/2412.14782
Autor:
Czédli, Gábor
Since Henrik Strietz's 1975 paper proving that the lattice Part($n$) of all partitions of an $n$-element finite set is four-generated, more than half a dozen papers have been devoted to four-element generating sets of this lattice. We prove that each
Externí odkaz:
http://arxiv.org/abs/2410.19650
Autor:
Czédli, Gábor
The block count of an equivalence $\mu\in$ Equ$(A)$ is the number blnum$(\mu)$ of blocks of (the partition corresponding to) $\mu$. We say that $X=\{\mu_1,\mu_2,\mu_3,\mu_4\}$ is a four-element generating set of Equ$(A)$ with consecutive block counts
Externí odkaz:
http://arxiv.org/abs/2410.15328
We introduce the notion of power lattices that unifies and extends the equicardinal geometric lattices, Cartesian products of subspace lattices, and multiset subset lattices, among several others. The notions of shellability for simplicial complexes,
Externí odkaz:
http://arxiv.org/abs/2407.08629
We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and Haviar (2015).
Externí odkaz:
http://arxiv.org/abs/2309.14127
We reinterpret the Rhodes semilattices $R_n(\mathfrak{G})$ of a group $\mathfrak{G}$ in terms of gain graphs and generalize them to all gain graphs, both as sets of partition-potential pairs and as sets of subgraphs, and for the latter, further to bi
Externí odkaz:
http://arxiv.org/abs/2309.02700
Autor:
Czédli, Gábor
Following G. Gr\"atzer and E. Knapp (2007), a slim semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no $M_3$ as a sublattice. An SPS lattice is a slim rectangular lattice if it has exactly two doubly irreducib
Externí odkaz:
http://arxiv.org/abs/2301.00401
Autor:
He, Peng, Wang, Xue-ping
In this article, we first characterize pseudocomplemented inductive modular lattices by using their two 0-sublattices. Then we use two 0-sublattices of a subgroup lattice to describe all locally cyclic abelian groups. In particular, we show that a lo
Externí odkaz:
http://arxiv.org/abs/2211.01337
Autor:
Czédli, Gábor
Slim semimodular lattices (for short, SPS lattices) and slim rectangular lattices (for short, SR lattices) were introduced by G. Gr\"atzer and E. Knapp in 2007 and 2009. These lattices are necessarily finite and planar, and they have been studied in
Externí odkaz:
http://arxiv.org/abs/2208.03606
Autor:
Czédli, Gábor
Since their introduction by G. Gr\"atzer and E. Knapp in 2007, more than four dozen papers have been devoted to finite slim planar semimodular lattices (in short, SPS lattices or slim semimodular lattices) and to some related fields. In addition to d
Externí odkaz:
http://arxiv.org/abs/2206.14769