M. Akian, S. Gaubert, and C. Walsh, Discrete max-plus spectral theory, Idempotent Mathematics and Mathematical Physics, pp.53-78, 2005.
DOI : 10.1090/conm/377/06984

URL : https://hal.archives-ouvertes.fr/inria-00000968

A. Bouillard and B. Gaujal, Coupling time of a (max,plus) matrix, Proceedings of the Workshop on Max-Plus Algebra at the 1st IFAC Symposium on System Structure and Control, 2001.
URL : https://hal.archives-ouvertes.fr/inria-00100573

A. Brauer, On a Problem of Partitions, American Journal of Mathematics, vol.64, issue.1/4, pp.299-312, 1942.
DOI : 10.2307/2371684

A. Richard, H. J. Brualdi, and . Ryser, Combinatorial matrix theory, 1991.

B. Charron-bost, M. Függer, and T. Nowak, New transience bounds for long walks, p.2012
URL : https://hal.archives-ouvertes.fr/hal-00993814

B. Charron-bost, M. Függer, J. L. Welch, and J. Widder, Full Reversal Routing as a Linear Dynamical System, Proceedings of the 18th International Colloquium on Structural Information and Communication Complexity (SIROCCO), pp.101-112, 2011.
DOI : 10.1007/BFb0022451

B. Charron-bost and T. Nowak, General transience bounds in tropical linear algebra via Nachtigall decomposition, Proceedings of the Workshop on Tropical and Idempotent Mathematics Institute for Information Transmission Problems of the Russian Academy of Sciences, pp.46-52
URL : https://hal.archives-ouvertes.fr/hal-00993902

P. Chrétienne, Chemins extr??maux d'un graphe doublement valu??, RAIRO - Operations Research, vol.18, issue.3, pp.221-245, 1984.
DOI : 10.1051/ro/1984180302211

G. Cohen, D. Dubois, J. Quadrat, and M. Viot, Analyse du comportement périodique de systèmes de production par la théorie des dio¨?desdio¨?des, INRIA Research Report, vol.191, 1983.

E. V. Denardo, Periods of Connected Networks and Powers of Nonnegative Matrices, Mathematics of Operations Research, vol.2, issue.1, pp.20-24, 1977.
DOI : 10.1287/moor.2.1.20

A. L. Dulmage and N. S. Mendelsohn, Gaps in the exponent set of primitive matrices, Illinois Journal of Mathematics, vol.8, issue.4, pp.642-656, 1964.

S. Even and S. Rajsbaum, The use of a synchronizer yields the maximum computation rate in distributed networks, Theory of Computing Systems, vol.5, issue.9, pp.447-474, 1997.
DOI : 10.1007/BF02679457

M. Hartmann and C. Arguelles, Transience Bounds for Long Walks, Mathematics of Operations Research, vol.24, issue.2, pp.414-439, 1999.
DOI : 10.1287/moor.24.2.414

K. H. Kim, An extension of the Dulmage-Mendelsohn theorem, Linear Algebra and its Applications, vol.27, pp.187-197, 1979.
DOI : 10.1016/0024-3795(79)90041-7

Q. Li and J. Shao, The index set problem for Boolean (or nonnegative) matrices, Discrete Mathematics, vol.123, issue.1-3, pp.1-3, 1993.
DOI : 10.1016/0012-365X(93)90008-H

Y. Malka, S. Moran, and S. Zaks, A lower bound on the period length of a distributed scheduler, Algorithmica, vol.29, issue.1, pp.383-398, 1993.
DOI : 10.1007/BF01769705

Y. Malka and S. Rajsbaum, Analysis of distributed algorithms based on recurrence relations, Proceedings of the 5th International Workshop on Distributed Algorithms (WDAG), pp.242-253, 1992.
DOI : 10.1007/BFb0022451

M. Molnárová, Computational Complexity of Nachtigall's Representation, Optimization, vol.8, issue.1, pp.93-101, 2003.
DOI : 10.1007/BF01199464

K. Nachtigall, Powers of matrices over an extremal algebra with applications to periodic graphs, Mathematical Methods of Operations Research, vol.2, issue.1, pp.87-102, 1997.
DOI : 10.1007/BF01199464

H. Schneider and M. H. Schneider, Max-Balancing Weighted Directed Graphs and Matrix Scaling, Mathematics of Operations Research, vol.16, issue.1, pp.208-222, 1991.
DOI : 10.1287/moor.16.1.208

S. Schwarz, On a sharp estimation in the theory of binary relations on a finite set, Czechoslovak Mathematical Journal, vol.20, issue.4, pp.703-714, 1970.

S. Serge? and H. Schneider, CSR expansions of matrix powers in max algebra, Transactions of the American Mathematical Society, vol.364, issue.11, pp.5969-5994, 2012.
DOI : 10.1090/S0002-9947-2012-05605-4

J. Shao and Q. Li, On the index of convergence of an irreducible Boolean matrix, Linear Algebra and Its Applications, vol.97, pp.185-210, 1987.

G. Soto-y-koelemeijer and T. Delft, On the behaviour of classes of min-max-plus systems, 2003.

H. Wielandt, . Unzerlegbare, and . Nicht-negative-matrizen, Unzerlegbare, nicht negative Matrizen, Mathematische Zeitschrift, vol.192, issue.1, pp.642-645, 1950.
DOI : 10.1007/BF02230720

. Laboratoire-d-'informatique and . Ecole-polytechnique, E-mail address: nowak@lix.polytechnique.fr CNRS, Laboratoire d, 91128.