Meet-distributive lattices have the intersection property

Henri Mühle

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 1, page 95-104
  • ISSN: 0862-7959

Abstract

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This paper is an erratum of H. Mühle: Distributive lattices have the intersection property, Math. Bohem. (2021). Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange property. Moreover, meet-distributive lattices are join semidistributive. Therefore, they admit two natural secondary structures: the core label order is an alternative order on the lattice elements and the canonical join complex is the flag simplicial complex on the canonical join representations. In this article we present a characterization of finite meet-distributive lattices in terms of the core label order and the canonical join complex, and we show that the core label order of a finite meet-distributive lattice is always a meet-semilattice.

How to cite

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Mühle, Henri. "Meet-distributive lattices have the intersection property." Mathematica Bohemica 148.1 (2023): 95-104. <http://eudml.org/doc/299446>.

@article{Mühle2023,
abstract = {This paper is an erratum of H. Mühle: Distributive lattices have the intersection property, Math. Bohem. (2021). Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange property. Moreover, meet-distributive lattices are join semidistributive. Therefore, they admit two natural secondary structures: the core label order is an alternative order on the lattice elements and the canonical join complex is the flag simplicial complex on the canonical join representations. In this article we present a characterization of finite meet-distributive lattices in terms of the core label order and the canonical join complex, and we show that the core label order of a finite meet-distributive lattice is always a meet-semilattice.},
author = {Mühle, Henri},
journal = {Mathematica Bohemica},
keywords = {meet-distributive lattice; congruence-uniform lattice; canonical join complex; core label order; intersection property},
language = {eng},
number = {1},
pages = {95-104},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Meet-distributive lattices have the intersection property},
url = {http://eudml.org/doc/299446},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Mühle, Henri
TI - Meet-distributive lattices have the intersection property
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 1
SP - 95
EP - 104
AB - This paper is an erratum of H. Mühle: Distributive lattices have the intersection property, Math. Bohem. (2021). Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange property. Moreover, meet-distributive lattices are join semidistributive. Therefore, they admit two natural secondary structures: the core label order is an alternative order on the lattice elements and the canonical join complex is the flag simplicial complex on the canonical join representations. In this article we present a characterization of finite meet-distributive lattices in terms of the core label order and the canonical join complex, and we show that the core label order of a finite meet-distributive lattice is always a meet-semilattice.
LA - eng
KW - meet-distributive lattice; congruence-uniform lattice; canonical join complex; core label order; intersection property
UR - http://eudml.org/doc/299446
ER -

References

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