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- W1597116596 abstract "Given an Iterated Function System (IFS) of topical maps verifying some conditions, we prove that the asymptotic height optimization problems are equivalent to finding the extrema of a continuous functional, the <italic>average height</italic>, on some compact space of measures. We give general results to determine these extrema, and then apply them to two concrete problems. First, we give a new proof of the theorem that the densest heaps of two Tetris pieces are sturmian. Second, we construct an explicit counterexample to the Lagarias-Wang finiteness conjecture for the joint spectral radius of a set of matrices. <sc>Résumé.</sc> Etant donné un système itéré de fonctions (IFS) topicales, vérifiant certaines conditions, nous montrons que les questions d’optimisation asymptotique de la hauteur sont équivalentes à la recherche des extrema d’une fonctionnelle continue, la <italic>hauteur moyenne</italic>, sur un certain espace compact de mesures. Nous présentons des résultats généraux permettant de déterminer ces extrema, puis appliquons ces méthodes à deux problèmes concrets. Premièrement, nous redémontrons que les empilements les plus denses de deux pièces de Tetris sont sturmiens. Deuxièmement, nous construisons un contre-exemple effectif à la conjecture de finitude de Lagarias et Wang sur le rayon spectral joint d’un ensemble de matrices." @default.
- W1597116596 created "2016-06-24" @default.
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- W1597116596 date "2001-09-10" @default.
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- W1597116596 title "Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture" @default.
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- W1597116596 doi "https://doi.org/10.1090/s0894-0347-01-00378-2" @default.
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