{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-G6IMMKZP/41598a71-d24d-4afd-9546-724b7d0e6d4f/PDF","dcterms:extent":"373 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-G6IMMKZP/1e8981fb-2799-485e-b4a5-e2d813bb5053/TEXT","dcterms:extent":"46 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-G6IMMKZP","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["Penttila, Tim","Siciliano, Alessandro"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:20"},{"@xml:lang":"sl","#text":"str. 51-68"}],"dc:identifier":["DOI:10.26493/1855-3974.1996.db7","ISSN:1855-3966","COBISSID_HOST:91102723","URN:URN:NBN:SI:doc-G6IMMKZP"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"diagram geometry"},{"@xml:lang":"sl","#text":"diagramska geometrija"},{"@xml:lang":"en","#text":"incidence map"},{"@xml:lang":"en","#text":"incidence structure"},{"@xml:lang":"sl","#text":"incidenčne strukture"},{"@xml:lang":"sl","#text":"incidenčni zemljevid"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the incidence map of incidence structures|"},"dc:description":[{"@xml:lang":"sl","#text":"By using elementary linear algebra methods we exploit properties of the incidence map of certain incidence structures with finite block sizes. We give new and simple proofs of theorems of W. M. Kantor Math. Z. 124, 315-318 (1972) and G. I. Lehrer Math. Z. 147, 287-299 (1976), and their infinitary version. Similar results are obtained also for diagrams geometries. By mean of an extension of Block's Lemma on the number of orbits of an automorphism group of an incidence structure, we give informations on the number of orbits of: a permutation group (of possible infinite degree) on subsets of finite size; a collineation group of a projective and affine space (of possible infinite dimension) over a finite field on subspaces of finite dimension; a group of isometries of a classical polar space (of possible infinite rank) over a finite field on totally isotropic subspaces (or singular in case of orthogonal spaces) of finite dimension. Furthermore, when the structure is finite and the associated incidence matrix has full rank, we give an alternative proof of a result of A. Camina and J. Siemons Linear Algebra Appl. 117, 25-34 (1989). We then deduce that certain families of incidence structures have no sharply transitive sets of automorphisms acting on blocks"},{"@xml:lang":"sl","#text":"Z uporabo metod elementarne linearne algebre raziščemo lastnosti incidenčnega zemljevida določenih incidenčnih struktur s končnimi velikostmi blokov. Predstavimo nove in enostavne dokaze izrekov Kantorja in Lehrerja, pa tudi njihovo neskončno različico. Podobne rezultate dobimo tudi za diagramske geometrije. S pomočjo razširitve Blockove leme o številu orbit grupe avtomorfizmov incidenčne strukture dobimo informacije o številu orbit naslednjih struktur: permutacijske grupe (lahko tudi neskončne stopnje) na podmnožicah končne velikosti; kolineacijske grupe projektivnega in afinega prostora (lahko tudi neskončne dimenzije) nad končnim poljem na podprostorih končne dimenzije; grupe izometrij klasičnega polarnega prostora (lahko tudi neskončnega ranga) nad končnim poljem na povsem izotropnih podprostorih (ali povsem singularnih v primeru ortogonalnega prostora) končnih dimenzij. Nadalje, za primer, ko je struktura končna, pridružena incidenčna matrika pa ima poln rang, predstavimo alternativen dokaz rezultata Camine in Siemonsa. Nato pokažemo, da določene družine incidenčnih struktur nimajo ostro tranzitivnih množic avtomorfizmov, ki bi delovali na blokih"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-G6IMMKZP","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-G6IMMKZP"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-G6IMMKZP/41598a71-d24d-4afd-9546-724b7d0e6d4f/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-G6IMMKZP/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-G6IMMKZP"}}}}