Two sided Sand Piles Model and unimodal sequences
RAIRO - Theoretical Informatics and Applications (2008)
- Volume: 42, Issue: 3, page 631-646
- ISSN: 0988-3754
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top- R. Anderson, L. Lovász, P. Shor, J. Spencer, E. Tardos, and S. Winograd. Disks, ball, and walls: analysis of a combinatorial game. Amer. Math. Monthly96 (1989) 481–493.
- P. Bak, C. Tang, and K. Wiesenfeld. Self-organized criticality. Phys. Rev. A38 (1988) 364–374.
- J. Bitar and E. Goles. Paralel chip firing games on graphs. Theoret. Comput. Sci.92 (1992) 291–300.
- A. Bjorner, L. Lovász, and W. Shor. Chip-firing games on graphes. Eur .J. Combin.12 (1991) 283–291.
- A. Bjorner and G. Ziegler. Introduction to greedoids. Matroid applications, N. White, Ed. Cambridge University Press (1991) 284–357.
- F. Brenti. Log-concave and unimodal sequences in algebra, combinatorics and geometry: an update. Contemporary Mathematics178 (1994) 71–84.
- T. Brylawski. The lattice of interger partitions. Discrete Mathematics6 (1973) 201–219.
- B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press (1990).
- E. Duchi, R. Mantaci, D. Rossin, and H.D. Phan. Bidimensional sand pile and ice pile models. PUMA 17 (2006) 71–96.
- E. Formenti, B. Masson, and T. Pisokas. Advances in symmetric sandpiles. Fundamenta Informaticae20 (2006) 1–22.
- E. Goles and M.A. Kiwi. Games on line graphes and sand piles. Theoret. Comput. Sci.115 (1993) 321–349.
- E. Goles, M. Morvan, and H.D. Phan. Lattice structure and convergence of a game of cards. Ann. Combin.6 (2002) 327–335.
- E. Goles, M. Morvan, and H.D. Phan. Sandpiles and order structure of integer partitions. Discrete Appl. Math.117 (2002) 51–64.
- C. Greene and D.J. Kleitman. Longest chains in the lattice of integer partitions ordered by majorization. Eur. J. Combin.7 (1986) 1–10.
- M. Latapy, R. Mantaci, M. Morvan, and H.D. Phan. Structure of some sand piles model. Theoret. Comput. Sci, 262 (2001) 525–556.
- M. Latapy and H.D. Phan. The lattice of integer partitions and its infinite extension. To appear in Discrete Mathematics (2008).
- Ha Duong Phan. PhD thesis. Université Paris VII (1999).
- J. Spencer. Balancing vectors in the max norm. Combinatorica6 (1986) 55–65.
- R. Stanley. Log-cocave and unimodal sequences in algebra, combinatorics and geometry. Graph theory and its applications: East and West (Jinan 1986). Ann. New York Acad. Sci.576 (1989).