{"?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-CHCF3586/0b63d4d7-e630-4475-b41c-ccc26dbce7b1/PDF","dcterms:extent":"527 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-CHCF3586/7eff735e-32d3-49ba-921b-deb1df2a8e90/TEXT","dcterms:extent":"75 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-CHCF3586","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["Wu, Yaokun","Zhu, Yinfeng"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"številka:4"},{"@xml:lang":"sl","#text":"str. 649-674"}],"dc:identifier":["DOI:10.26493/1855-3974.1753.52a","COBISSID_HOST:142185731","ISSN:1855-3966","URN:URN:NBN:SI:doc-CHCF3586"],"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":"incidence operator"},{"@xml:lang":"sl","#text":"incidenčni operator"},{"@xml:lang":"sl","#text":"jedrni prostor"},{"@xml:lang":"en","#text":"kernel space"},{"@xml:lang":"sl","#text":"krepka oblika"},{"@xml:lang":"sl","#text":"ovrednotena delno urejena množica"},{"@xml:lang":"sl","#text":"rang"},{"@xml:lang":"en","#text":"rank"},{"@xml:lang":"en","#text":"strong shape"},{"@xml:lang":"sl","#text":"šibka oblika"},{"@xml:lang":"en","#text":"valuated poset"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Top-heavy phenomena for transformations|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$S$? be a transformation semigroup acting on a set ?$\\Omega$?. The action of ?$S$? on ?$\\Omega$? can be naturally extended to be an action on all subsets of ?$\\Omega$?. We say that ?$S$? is ?$\\ell$?-homogeneous provided it can send ?$A$? to ?$B$? for any two (not necessarily distinct) ?$\\ell$?-subsets ?$A$? and ?$B$? of ?$\\Omega$?. On the condition that ?$k \\le \\ell < k + \\ell \\le |\\Omega|$?, we show that every ?$\\ell$?-homogeneous transformation semigroup acting on ?$\\Omega$? must be ?$k$?-homogeneous. We report other variants of this result for Boolean semirings and affine/projective geometries. In general, any semigroup action on a poset gives rise to an automaton and we associate some sequences of integers with the phase space of this automaton. When this poset is a geometric lattice, we propose to investigate various possible regularity properties of these sequences, especially the so-called top-heavy property. In the course of this study, we are led to a conjecture about the injectivity of the incidence operator of a geometric lattice, generalizing a conjecture of Kung"},{"@xml:lang":"sl","#text":"Naj bo ?$S$? transformacijska polgrupa, delujoča na množici ?$\\Omega$?. Delovanje ?$S$? na ?$\\Omega$? se da naravno razširiti do delovanja na vseh podmnožicah množice ?$\\Omega$?. Pravimo, da je ?$S$? ?$\\ell$?-homogena, če lahko preslika ?$A$? v ?$B$?, kjer sta ?$A$? in ?$B$? poljubni dve (ne nujno različni) ?$\\ell$?-podmnožici množice ?$\\Omega$?. Dokažemo, da je pri pogoju ?$k \\le \\ell < k + \\ell \\le |\\Omega|$? vsaka ?$\\ell$?-homogena transformacijska polgrupa, ki deluje na ?$\\Omega$?, ?$k$?-homogena. Poročamo o drugih različicah tega rezultata za Booleove polkolobarje in afine/projektivne geometrije. V splošnem, vsako delovanje polgrupe na delno urejeni množici porodi nek avtomat; faznemu prostoru tega avtomata priredimo določena celoštevilska zaporedja. V primeru, ko je ta delno urejena množica geometrijska mreža, raziskujemo različne regularnostne lastnosti teh zaporedij, še posebej t.i. lastnost zgornje obtežitve. Med raziskavo smo prišli do domneve o injektivnosti incidenčnega operatorja geometrijske mreže, ki posplošuje Kungovo domnevo"}],"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-CHCF3586","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-CHCF3586"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-CHCF3586/0b63d4d7-e630-4475-b41c-ccc26dbce7b1/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-CHCF3586/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-CHCF3586"}}}}