Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture
HTML articles powered by AMS MathViewer

by Thierry Bousch and Jean Mairesse
J. Amer. Math. Soc. 15 (2002), 77-111
Published electronically: September 10, 2001


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 average height, 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.

Résumé. 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 hauteur moyenne, 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.

Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 49J27, 37D35
  • Retrieve articles in all journals with MSC (2000): 49J27, 37D35
Bibliographic Information
  • Thierry Bousch
  • Affiliation: Laboratoire de Mathématique (UMR 8628 du CNRS), bât. 425, Université de Paris-Sud, 91405 Orsay Cedex, France
  • Email:
  • Jean Mairesse
  • Affiliation: LIAFA, CNRS et Université Paris 7, case 7014, 2 place Jussieu, 75251 Paris Cedex 05, France
  • Email:
  • Received by editor(s): July 11, 2000
  • Published electronically: September 10, 2001
  • Additional Notes: The work of the second author was partially supported by the European Community Framework IV programme through the research network ALAPEDES (“The ALgebraic Approach to Performance Evaluation of Discrete Event Systems”)
  • © Copyright 2001 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 15 (2002), 77-111
  • MSC (2000): Primary 49J27, 37D35
  • DOI:
  • MathSciNet review: 1862798