@prefix dcat: . @prefix dct: . @prefix foaf: . @prefix vcard: . @prefix xsd: . a dcat:Dataset ; dct:description """ This thesis concerns hyperbolic Coxeter polytopes, their reflection groups and associated combinatorial and geometric invariants. Given a Coxeter group $G$ realisable as a discrete subgroup of $\\mathrm{Isom}\\,\\mathbb{H}^n$, there is a fundamental domain $\\mathscr{P} \\subset \\mathbb{H}^n$ naturally associated to it. The domain $\\mathscr{P}$ is a Coxeter polytope. Vice versa, given a Coxeter polytope $\\mathscr{P}$, the set of reflections in its facets generates a Coxeter group acting on $\\mathbb{H}^n$. The reflections give a natural set $S$ of generators for the group $G$. Then we can express the growth series $f_{(G,S)}(t)$ of the group $G$ with respect to the generating set $S$. By a result of R.~Steinberg, the corresponding growth series is the power series of a rational function. The growth rate $\\tau$ of $G$ is the reciprocal to the radius of convergence of such a series. The growth rate is an algebraic integer and, by a result of J.~Milnor, $\\tau > 1$. By a result of W.~Parry, if $G$ acts on $\\mathbb{H}^n$, $n=2,3$, cocompactly, then its growth rate is a Salem number. By a result of W.~Floyd, there is a geometric correspondence between the growth rates of cocompact and finite co-volume Coxeter groups acting on $\\mathbb{H}^2$. This correspondence gives a geometric picture for the convergence of Salem numbers to Pisot numbers. There, Pisot numbers correspond to the growth rates of finite-volume polygons with ideal vertices. We reveal an analogous phenomenon in dimension $3$ by considering degenerations of compact Coxeter polytopes to finite-volume Coxeter polytopes with four-valent ideal vertices. In dimension $n\\geq 4$, the growth rate of a Coxeter group $G$ acting cocompactly on $\\mathbb{H}^n$ is known to be neither a Salem, nor a Pisot number. A particularly interesting class of Coxeter groups are right-angled Coxeter groups. In the case of a right-angled Coxeter group acting on $\\mathbb{H}^n$, its fundamental domain $\\mathscr{P} \\subset \\mathbb{H}^n$ is a right-angled polytope. Concerning the class of right-angled polytopes in $\\mathbb{H}^4$ (compact, finite volume or ideal, as subclasses), the following questions emerge: \\begin{enumerate} \\item[-] what are minimal volume polytopes in these families? \\item[-] what are polytopes with minimal number of combinatorial compounds (facets, faces, edges, vertices) in these families? \\end{enumerate} Various results concerning the above questions in the case of finite-volume right-angled polytopes were obtained by \\'{E}.~Vinberg, L.~Potyaga\\u{\\i}lo and recently by B.~Everitt, J.~Ratcliffe, S.~Tschantz. In the case of compact right-angled polytopes the answer is conjectured by \\'{E}.~Vinberg and L.~Potyaga\\u{\\i}lo. In this thesis, the above questions in the case of ideal right-angled polytopes are considered and completely answered. We conclude with some partial results concerning the case of compact right-angled polytopes. """ ; dct:identifier "tel-00762315" ; dct:issued "2026-06-01T12:09:44.031676"^^xsd:dateTime ; dct:language "en" ; dct:modified "2026-06-01T12:09:44.031683"^^xsd:dateTime ; dct:publisher ; dct:title "On extremal properties of hyperbolic Coxeter polytopes and their reflection groups" ; dcat:contactPoint [ a vcard:Organization ; vcard:fn "CCSD" ] ; dcat:distribution ; dcat:keyword "coxeter-group", "groupe-de-coxeter", "growth-rate", "growth-series", "hyperbolic-polytope", "infoeu-reposemanticsdoctoralthesis", "mathmath-comathematics-mathcombinatorics-mathco", "mathmath-grmathematics-mathgroup-theory-mathgr", "mathmath-mgmathematics-mathmetric-geometry-mathmg", "mathmath-ntmathematics-mathnumber-theory-mathnt", "nombre-de-pisot", "nombre-de-salem", "pisot-number", "polyedre-hyperbolique", "salem-number", "serie-daccroissement", "taux-daccroissement", "theses" ; dcat:landingPage . a dcat:Distribution ; dct:format "HTML" ; dct:issued "2026-06-01T12:09:44.205054"^^xsd:dateTime ; dct:modified "2026-06-01T12:09:43.969957"^^xsd:dateTime ; dct:title "On extremal properties of hyperbolic Coxeter polytopes and their reflection groups" ; dcat:accessURL . a foaf:Agent ; foaf:name "test_moissonnage_selune" . a foaf:Document .