CYCLIC AND ROTATIONAL LATIN HYBRID TRIPLE SYSTEMS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10372212" target="_blank" >RIV/00216208:11320/17:10372212 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1515/ms-2017-0032" target="_blank" >http://dx.doi.org/10.1515/ms-2017-0032</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1515/ms-2017-0032" target="_blank" >10.1515/ms-2017-0032</a>

Jazyk výsledku

angličtina

Název v původním jazyce

CYCLIC AND ROTATIONAL LATIN HYBRID TRIPLE SYSTEMS

Popis výsledku v původním jazyce

It is well known that given a Steiner triple system (STS) one can define a binary operation ASTERISK OPERATOR upon its base set by assigning x ASTERISK OPERATOR x = x for all x and x ASTERISK OPERATOR 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 (MTS), directed triple systems (DTS) as well as hybrid triple systems (HTS), where (x, y) is considered to be ordered. In the case of STSs and MTSs the operation yields a quasigroup, however this is not necessarily the case for DTSs and HTSs. A DTS or an HTS which induces a quasigroup is said to be Latin. In this paper we study Latin DTSs and Latin HTSs which admit a cyclic or a 1-rotational automorphism. We prove the existence spectra for these systems as well as the existence spectra for their pure variants. As a side result we also obtain the existence spectra of pure cyclic and pure 1-rotational MTSs.

Název v anglickém jazyce

CYCLIC AND ROTATIONAL LATIN HYBRID TRIPLE SYSTEMS

Popis výsledku anglicky

It is well known that given a Steiner triple system (STS) one can define a binary operation ASTERISK OPERATOR upon its base set by assigning x ASTERISK OPERATOR x = x for all x and x ASTERISK OPERATOR 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 (MTS), directed triple systems (DTS) as well as hybrid triple systems (HTS), where (x, y) is considered to be ordered. In the case of STSs and MTSs the operation yields a quasigroup, however this is not necessarily the case for DTSs and HTSs. A DTS or an HTS which induces a quasigroup is said to be Latin. In this paper we study Latin DTSs and Latin HTSs which admit a cyclic or a 1-rotational automorphism. We prove the existence spectra for these systems as well as the existence spectra for their pure variants. As a side result we also obtain the existence spectra of pure cyclic and pure 1-rotational MTSs.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

—

Svazek periodika

2017

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

18

Strana od-do

1055-1072

Kód UT WoS článku

000414656000001

EID výsledku v databázi Scopus

—