FMF, Mathematical Library, Lj. (MAKLJ)
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Top-heavy phenomena for transformationsWu, Yaokun ; Zhu, YinfengNaj 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.Source: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 22, no. 4, 2022, str. 649-674)Type of material - article, component part ; adult, seriousPublish date - 2022Language - englishCOBISS.SI-ID - 142185731
Author
Wu, Yaokun |
Zhu, Yinfeng
Topics
incidenčni operator |
jedrni prostor |
rang |
krepka oblika |
ovrednotena delno urejena množica |
šibka oblika |
incidence operator |
kernel space |
rank |
strong shape |
valuated poset
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Wu, Yaokun | |
Zhu, Yinfeng |
Source: Personal bibliographies
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