Triple systems and binary operations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10287285" target="_blank" >RIV/00216208:11320/14:10287285 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.disc.2014.02.007" target="_blank" >http://dx.doi.org/10.1016/j.disc.2014.02.007</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.disc.2014.02.007" target="_blank" >10.1016/j.disc.2014.02.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Triple systems and binary operations

Popis výsledku v původním jazyce

It is well known that given a Steiner triple system (STS) one can define a binary operation * upon its base set by assigning x * x = x for all x and x * y = z, where z is the third point in the block containing the pair {x, y}. The same can be done for Mendelsohn triple systems (MTSs) as well as hybrid triple systems (HTSs), where (x, y) is considered to be ordered. In the case of STSs and MTSs, the operation is a quasigroup, however this is not necessarily the case for HTSs. In this paper we study thebinary operation induced by HTSs. It turns out that each such operation * satisfies y is an element of {x * (x * y), (x * y) * x} and y is an element of {(y * x) * x, x * (y * x)} for all x and y from the base set. We call every binary operation that fulfils this condition hybridly symmetric. Not all idempotent hybridly symmetric operations can be obtained from HTSs. We show that these operations correspond to decompositions of a complete digraph into certain digraphs on three vertices.

Název v anglickém jazyce

Triple systems and binary operations

Popis výsledku anglicky

It is well known that given a Steiner triple system (STS) one can define a binary operation * upon its base set by assigning x * x = x for all x and x * y = z, where z is the third point in the block containing the pair {x, y}. The same can be done for Mendelsohn triple systems (MTSs) as well as hybrid triple systems (HTSs), where (x, y) is considered to be ordered. In the case of STSs and MTSs, the operation is a quasigroup, however this is not necessarily the case for HTSs. In this paper we study thebinary operation induced by HTSs. It turns out that each such operation * satisfies y is an element of {x * (x * y), (x * y) * x} and y is an element of {(y * x) * x, x * (y * x)} for all x and y from the base set. We call every binary operation that fulfils this condition hybridly symmetric. Not all idempotent hybridly symmetric operations can be obtained from HTSs. We show that these operations correspond to decompositions of a complete digraph into certain digraphs on three vertices.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Discrete Mathematics

ISSN

0012-365X

e-ISSN

—

Svazek periodika

2014

Číslo periodika v rámci svazku

323

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

1-11

Kód UT WoS článku

000335203000001

EID výsledku v databázi Scopus

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