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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Submaximal clones over a three-element set up to minor-equivalence
Original language description
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 <= (m) D if there exists a minor homomorphism from C to D. We show that the aforementioned poset has only three submaximal elements.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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