Matches in SemOpenAlex for { <https://semopenalex.org/work/W2950470601> ?p ?o ?g. }
Showing items 1 to 79 of
79
with 100 items per page.
- W2950470601 abstract "Let $Omega$ be a set of cardinality $n$, $G$ a permutation group on $Omega$, and $f:OmegatoOmega$ a map which is not a permutation. We say that $G$ synchronizes $f$ if the semigroup $langle G,frangle$ contains a constant map. The first author has conjectured that a primitive group synchronizes any map whose kernel is non-uniform. Rystsov proved one instance of this conjecture, namely, degree $n$ primitive groups synchronize maps of rank $n-1$ (thus, maps with kernel type $(2,1,ldots,1)$). We prove some extensions of Rystsov's result, including this: a primitive group synchronizes every map whose kernel type is $(k,1,ldots,1)$. Incidentally this result provides a new characterization of imprimitive groups. We also prove that the conjecture above holds for maps of extreme ranks, that is, ranks 3, 4 and $n-2$. These proofs use a graph-theoretic technique due to the second author: a transformation semigroup fails to contain a constant map if and only if it is contained in the endomorphism semigroup of a non-null (simple undircted) graph. The paper finishes with a number of open problems, whose solutions will certainly require very delicate graph theoretical considerations." @default.
- W2950470601 created "2019-06-27" @default.
- W2950470601 creator A5031014269 @default.
- W2950470601 creator A5048639170 @default.
- W2950470601 date "2013-06-20" @default.
- W2950470601 modified "2023-09-28" @default.
- W2950470601 title "Primitive Groups Synchronize Non-uniform Maps of Extreme Ranks" @default.
- W2950470601 cites W138672376 @default.
- W2950470601 cites W1965325185 @default.
- W2950470601 cites W1995452723 @default.
- W2950470601 cites W2001279658 @default.
- W2950470601 cites W2058407845 @default.
- W2950470601 cites W2078436604 @default.
- W2950470601 cites W2086132675 @default.
- W2950470601 cites W2115279247 @default.
- W2950470601 cites W2118209939 @default.
- W2950470601 cites W2142561347 @default.
- W2950470601 cites W2147563970 @default.
- W2950470601 cites W2149113716 @default.
- W2950470601 cites W2167971415 @default.
- W2950470601 cites W2287978812 @default.
- W2950470601 cites W2323769209 @default.
- W2950470601 cites W2953025266 @default.
- W2950470601 hasPublicationYear "2013" @default.
- W2950470601 type Work @default.
- W2950470601 sameAs 2950470601 @default.
- W2950470601 citedByCount "0" @default.
- W2950470601 crossrefType "posted-content" @default.
- W2950470601 hasAuthorship W2950470601A5031014269 @default.
- W2950470601 hasAuthorship W2950470601A5048639170 @default.
- W2950470601 hasConcept C108710211 @default.
- W2950470601 hasConcept C114614502 @default.
- W2950470601 hasConcept C116858840 @default.
- W2950470601 hasConcept C118615104 @default.
- W2950470601 hasConcept C132525143 @default.
- W2950470601 hasConcept C164226766 @default.
- W2950470601 hasConcept C207405024 @default.
- W2950470601 hasConcept C2524010 @default.
- W2950470601 hasConcept C2780990831 @default.
- W2950470601 hasConcept C33923547 @default.
- W2950470601 hasConcept C74193536 @default.
- W2950470601 hasConceptScore W2950470601C108710211 @default.
- W2950470601 hasConceptScore W2950470601C114614502 @default.
- W2950470601 hasConceptScore W2950470601C116858840 @default.
- W2950470601 hasConceptScore W2950470601C118615104 @default.
- W2950470601 hasConceptScore W2950470601C132525143 @default.
- W2950470601 hasConceptScore W2950470601C164226766 @default.
- W2950470601 hasConceptScore W2950470601C207405024 @default.
- W2950470601 hasConceptScore W2950470601C2524010 @default.
- W2950470601 hasConceptScore W2950470601C2780990831 @default.
- W2950470601 hasConceptScore W2950470601C33923547 @default.
- W2950470601 hasConceptScore W2950470601C74193536 @default.
- W2950470601 hasLocation W29504706011 @default.
- W2950470601 hasOpenAccess W2950470601 @default.
- W2950470601 hasPrimaryLocation W29504706011 @default.
- W2950470601 hasRelatedWork W1965339293 @default.
- W2950470601 hasRelatedWork W1967932087 @default.
- W2950470601 hasRelatedWork W2045746486 @default.
- W2950470601 hasRelatedWork W2051870651 @default.
- W2950470601 hasRelatedWork W2057527818 @default.
- W2950470601 hasRelatedWork W2078824781 @default.
- W2950470601 hasRelatedWork W2081572779 @default.
- W2950470601 hasRelatedWork W2329152253 @default.
- W2950470601 hasRelatedWork W2330993403 @default.
- W2950470601 hasRelatedWork W2604528540 @default.
- W2950470601 hasRelatedWork W2911922132 @default.
- W2950470601 hasRelatedWork W2949927077 @default.
- W2950470601 hasRelatedWork W2964047154 @default.
- W2950470601 hasRelatedWork W2971721948 @default.
- W2950470601 hasRelatedWork W3038109304 @default.
- W2950470601 hasRelatedWork W3102040219 @default.
- W2950470601 hasRelatedWork W3165382499 @default.
- W2950470601 hasRelatedWork W3178944103 @default.
- W2950470601 hasRelatedWork W3198948812 @default.
- W2950470601 hasRelatedWork W341126498 @default.
- W2950470601 isParatext "false" @default.
- W2950470601 isRetracted "false" @default.
- W2950470601 magId "2950470601" @default.
- W2950470601 workType "article" @default.