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A CAT algorithm for the exhaustive generation of ice piles

Published online by Cambridge University Press:  28 February 2011

Paolo Massazza  and
Roberto Radicioni
Paolo Massazza
Affiliation:
Università degli Studi dell'Insubria, Dipartimento di Informatica e Comunicazione, Via Mazzini 5, 21100 Varese, Italy; {paolo.massazza,roberto.radicioni}@uninsubria.it
Roberto Radicioni
Affiliation:
Università degli Studi dell'Insubria, Dipartimento di Informatica e Comunicazione, Via Mazzini 5, 21100 Varese, Italy; {paolo.massazza,roberto.radicioni}@uninsubria.it
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Abstract

We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model$\mbox{IPM}_k$(n), a generalization of the sand pile model$\mbox{SPM}$(n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice $\mbox{IPM}_k$(n): this lets us design an algorithm which generates all the ice piles of $\mbox{IPM}_k$(n) in amortized time O(1) and in space O($\sqrt n$).

Keywords

Sand pile modelice pile modelinteger partitionsexhaustive generationCAT algorithmsdiscrete dynamical systems
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 4 , October 2010 , pp. 525 - 543
Copyright
© EDP Sciences, 2011

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References

Bak, P., Tang, C. and Wiesenfeld, K., Self-organized criticality. Phys. Rev. A 38 (1988) 364–374. CrossRef
Brylawski, T., The lattice of integer partitions. Discrete Math. 6 (1973) 201–219. CrossRef
Corteel, S. and Gouyou-Beauchamps, D., Enumeration of sand piles. Discrete Math. 256 (2002) 625–643. CrossRef
Duchi, E., Mantaci, R., Phan, H.D. and Rossin, D., Bidimensional sand pile and ice pile models. PU.M.A. 17 (2007) 71–96.
Goles, E. and Kiwi, M.A., Games on line graphs and sand piles. Theoret. Comput. Sci. 115 (1993) 321–349. CrossRef
Goles, E., Morvan, M. and Phan, H.D., Sandpiles and order structure of integer partitions. Discrete Appl. Math. 117 (2002) 51–64. CrossRef
Latapy, M., Mantaci, R., Morvan, M. and Phan, H.D., Structure of same sand piles model. Theoret. Comput. Sci. 262 (2001) 525–556. CrossRef
Massazza, P., CAT, A algorithm for sand piles. PU.M.A. 19 (2008) 147–158.