TY - JOUR
T1 - Sandpiles and order structure of integer partitions
AU - Goles, Eric
AU - Morvan, Michel
AU - Phan, Ha Duong
N1 - Funding Information:
This work was done during M.M and H.D.P's visit at Departamento de Ingenierı́a Matemática, Universidad de Chile and was supported by Project ECOS-C96E02 and Chilean program FONDAP in Applied Mathematics (E.G., M.M., H.D.P.)
PY - 2002/3/15
Y1 - 2002/3/15
N2 - In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of L B, lattice of integer partitions introduced in Brylawski (Discrete Math. 6 (1973) 201), and we deduce from that a characterization of their fixed point. We prove that these orders form an increasing sequence of lattices from SPM to L B. We then characterize longest paths in these lattices and give a formula describing their length.
AB - In this paper, we study the orders obtained by the generalized dynamics of the sand piles model (SPM). We show that these orders are suborders of L B, lattice of integer partitions introduced in Brylawski (Discrete Math. 6 (1973) 201), and we deduce from that a characterization of their fixed point. We prove that these orders form an increasing sequence of lattices from SPM to L B. We then characterize longest paths in these lattices and give a formula describing their length.
UR - http://www.scopus.com/inward/record.url?scp=84867945528&partnerID=8YFLogxK
U2 - 10.1016/S0166-218X(01)00178-0
DO - 10.1016/S0166-218X(01)00178-0
M3 - Article
AN - SCOPUS:84867945528
SN - 0166-218X
VL - 117
SP - 51
EP - 64
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 1-3
ER -