ISSN 2590-9770
The Art of Discrete and Applied Mathematics 2 (2019) #P2.06
https://doi.org/10.26493/2590-9770.1333.152
(Also available at http://adam-journal.eu)
Regular antilattices
Karin Cvetko-Vah ∗
Department of Mathematics, Faculty of Mathematics and Physics,
University of Ljubljana, Jadranska 21, SI-1000 Ljubljana, Slovenia
Michael Kinyon †
Department of Mathematics, University of Denver, Denver, CO 80208, USA
Jonathan Leech
Department of Mathematics, Westmont College, Santa Barbara, CA 93108, USA
Tomaž Pisanski ‡
Faculty of Mathematics, Natural Sciences and Information Technologies,
University of Primorska, Glagoljaška 8, SI-6000 Koper, Slovenia, and
Andrej Marušič Institute, University of Primorska,
Muzejski trg 2, SI-6000 Koper, Slovenia, and
Faculty of Mathematics and Physics, University of Ljubljana,
Jadranska 21, SI-1000 Ljubljana, Slovenia, and
Institute of Mathematics, Physics and Mechanics (IMFM),
Jadranska 19, SI-1000 Ljubljana, Slovenia
Received 18 November 2019, accepted 21 December 2019, published online 30 December 2019
Abstract
Antilattices (S;∨,∧) for which the Green’s equivalences L(∨), R(∨), L(∧) and R(∧)
are all congruences of the entire antilattice are studied and enumerated.
Keywords: Noncommutative lattice, antilattice, Green’s equivalences, lattice of subvarieties, enumer-
ation, partition, composition.
Math. Subj. Class.: 06B75, 05A15, 05A17, 03G10, 11P99
∗Corresponding author.
†Michael Kinyon was supported by the Simons Foundation Collaboration Grant 359872.
‡Work of Tomaž Pisanski is supported in part by the ARRS grants P1-0294, J1-7051, N1-0032, and J1-9187.
E-mail addresses: karin.cvetko@fmf.uni-lj.si (Karin Cvetko-Vah), michael.kinyon@du.edu (Michael
Kinyon), leech@westmont.edu (Jonathan Leech), pisanski@upr.si (Tomaž Pisanski)
cb This work is licensed under https://creativecommons.org/licenses/by/4.0/
ISSN 2590-9770
The Art of Discrete and Applied Mathematics 2 (2019) #P2.06
https://doi.org/10.26493/2590-9770.1333.152
(Dostopno tudi na http://adam-journal.eu)
Regularne antimreže
Karin Cvetko-Vah ∗
Department of Mathematics, Faculty of Mathematics and Physics,
University of Ljubljana, Jadranska 21, SI-1000 Ljubljana, Slovenia
Michael Kinyon †
Department of Mathematics, University of Denver, Denver, CO 80208, USA
Jonathan Leech
Department of Mathematics, Westmont College, Santa Barbara, CA 93108, USA
Tomaž Pisanski ‡
Faculty of Mathematics, Natural Sciences and Information Technologies,
University of Primorska, Glagoljaška 8, SI-6000 Koper, Slovenia, and
Andrej Marušič Institute, University of Primorska,
Muzejski trg 2, SI-6000 Koper, Slovenia, and
Faculty of Mathematics and Physics, University of Ljubljana,
Jadranska 21, SI-1000 Ljubljana, Slovenia, and
Institute of Mathematics, Physics and Mechanics (IMFM),
Jadranska 19, SI-1000 Ljubljana, Slovenia
Prejeto 18. novembra 2019, sprejeto 21. decembra 2019, objavljeno na spletu 30. decembra 2019
Povzetek
Obravnavamo in preštevamo antimreže (S;∨,∧), za katere so Greenove ekvivalence
L(∨), R(∨), L(∧) in R(∧) tudi kongruence na celotni antimreži.
Ključne besede: Nekomutativna mreža, antimreža, Greenove ekvivalence, mreža podraznoterosti,
preštevanje, particija, kompozicija.
Math. Subj. Class.: 06B75, 05A15, 05A17, 03G10, 11P99
∗Kontaktni avtor.
†Michael Kinyon je bil podprt s strani Simons Foundation Collaboration, dotacija 359872.
‡Delo Tomaža Pisanskega je delno podprto s strani ARRS, dotacije P1-0294, J1-7051, N1-0032 in J1-9187.
E-poštni naslovi: karin.cvetko@fmf.uni-lj.si (Karin Cvetko-Vah), michael.kinyon@du.edu (Michael
Kinyon), leech@westmont.edu (Jonathan Leech), pisanski@upr.si (Tomaž Pisanski)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/