ISSN 2590-9770
The Art of Discrete and Applied Mathematics 2 (2019) #P2.09
https://doi.org/10.26493/2590-9770.1332.594
(Also available at http://adam-journal.eu)
Open problems from NCS 2018
Jonathan Leech
Westmont College Santa Barbara, CA, USA
João Pita Costa ∗
Jožef Stefan Institute, Ljubljana, Slovenia
Received 14 July 2019, accepted 19 September 2019, published online 31 December 2019
Abstract
All participants in the workshop NCS 2018 were invited to submit a list of open prob-
lems, typically problems relevant to the subject matter of their talk. These problems follow,
grouped according the particular individual presenting them. These individuals appear with
their problem sets in alphabetical order, the sole exception being that the Honoree of the
workshop appears first. Some of the presenters give a bit of background to accompany their
problems. In other cases, such as myself, the presenter assumes that enough background
was given in their talk as published herein. Thus the reader is invited to refer back to the
relevant article. It is hoped that in the months to follow some of these problems will be
solved, or at least, considerable light will be shed on them.
Keywords: Skew lattice, ring, primitive skew lattice, dual congruence distributivity, orthodox semi-
group, sheaf representation, left regular band, quasilattice, paralattice, covering lattice, skew Bool-
ean algebra, congruence lattice, antilattice, skew Heyting algebra, coset structure, comodernistic
lattice.
Math. Subj. Class.: 06A75, 06B20, 06B75
∗The author thanks the support of the Croatian Science Foundation’s funding of the project EVOSOFT, with
the reference UIP-2014-09-7945.
E-mail addresses: leech@westmont.edu (Jonathan Leech), joao.pitacosta@ijs.si (João Pita Costa)
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) #P2.09
https://doi.org/10.26493/2590-9770.1332.594
(Dostopno tudi na http://adam-journal.eu)
Odprti problemi z NCS 2018
Jonathan Leech
Westmont College Santa Barbara, CA, USA
João Pita Costa ∗
Jožef Stefan Institute, Ljubljana, Slovenia
Prejeto 14. julija 2019, sprejeto 19. septembra 2019, objavljeno na spletu 31. decembra 2019
Povzetek
Vsi udeleženci delavnice NCS 2018 so bili povabljeni, da predložijo seznam odprtih
problemov, praviloma vezanih na njihovo predavanje. Navedeni so prejeti problemi, ki
so združeni v sklope glede na posameznika, ki jih je predstavil. Ti sklopi so razvrščeni
po abecednem vrstnem redu glede na ime avtorja, z izjemo sklopa častnega udeleženca,
ki nastopa prvi. Nekateri udeleženci so svoje probleme opremili z ozadjem. V drugih
primerih, kakor denimo v mojem, avtor predpostavlja, da je ozadje v zadostnem obsegu
podano v predavanju, ki je objavljeno na tem mestu. Bralca torej vabimo, da primerja
problem z ustreznim člankom. Upamo, da bodo navedeni problemi rešeni v prihodnjih
mesecih, oziroma da bo vsaj prišlo do znatnih novih uvidov vanje.
Ključne besede: Poševna mreža, kolobar, primitivna poševna mreža, dualna kongruenčna distribu-
tivnost, ortodoksna polgrupa, upodobitev s snopi, levo regularen pas, kvazimreža, paramreža, krovna
mreža, poševna Boolova algebra, kongruenčna mreža, antimreža, poševna Heytingova algebra, odse-
kovna struktura, komodernistična mreža.
Math. Subj. Class.: 06A75, 06B20, 06B75
∗Avtor se zahvaljuje za podporo s strani Croatian Science Foundation pri financiranju projekta EVOSOFT,
referenčna oznaka UIP-2014-09-7945.
E-poštna naslova: leech@westmont.edu (Jonathan Leech), joao.pitacosta@ijs.si (João Pita Costa)
cb To delo je objavljeno pod licenco https://creativecommons.org/licenses/by/4.0/