Submaximal clones over a three-element set up to minor-equivalence

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489635" target="_blank" >RIV/00216208:11320/24:10489635 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=bP~wV66Bku" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=bP~wV66Bku</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00012-024-00852-w" target="_blank" >10.1007/s00012-024-00852-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Submaximal clones over a three-element set up to minor-equivalence

Popis výsledku v původním jazyce

We study clones modulo minor homomorphisms, which are mappings from one clone to another preserving arities of operations and respecting permutation and identification of variables. Minor-equivalent clones satisfy the same sets of identities of the form f(x(1),..., x(n)) approximate to g(y(1),..., y(m)), also known as minor identities, and therefore share many algebraic properties. Moreover, it was proved that the complexity of the CSP of a finite structure A only depends on the set of minor identities satisfied by the polymorphism clone of A. In this article we consider the poset that arises by considering all clones over a three-element set with the following order: we write C &lt;= (m) D if there exists a minor homomorphism from C to D. We show that the aforementioned poset has only three submaximal elements.

Název v anglickém jazyce

Submaximal clones over a three-element set up to minor-equivalence

Popis výsledku anglicky

We study clones modulo minor homomorphisms, which are mappings from one clone to another preserving arities of operations and respecting permutation and identification of variables. Minor-equivalent clones satisfy the same sets of identities of the form f(x(1),..., x(n)) approximate to g(y(1),..., y(m)), also known as minor identities, and therefore share many algebraic properties. Moreover, it was proved that the complexity of the CSP of a finite structure A only depends on the set of minor identities satisfied by the polymorphism clone of A. In this article we consider the poset that arises by considering all clones over a three-element set with the following order: we write C &lt;= (m) D if there exists a minor homomorphism from C to D. We show that the aforementioned poset has only three submaximal elements.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Algebra Universalis

ISSN

0002-5240

e-ISSN

1420-8911

Svazek periodika

85

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

31

Strana od-do

22

Kód UT WoS článku

001186652800002

EID výsledku v databázi Scopus

2-s2.0-85188137548