# A CAT algorithm for the exhaustive generation of ice piles

Paolo Massazza; Roberto Radicioni

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2010)

- Volume: 44, Issue: 4, page 525-543
- ISSN: 0988-3754

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topMassazza, Paolo, and Radicioni, Roberto. "A CAT algorithm for the exhaustive generation of ice piles." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 44.4 (2010): 525-543. <http://eudml.org/doc/246010>.

@article{Massazza2010,

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($\sqrt\{n\}$).},

author = {Massazza, Paolo, Radicioni, Roberto},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {sand pile model; ice pile model; integer partitions; exhaustive generation; CAT algorithms; discrete dynamical systems},

language = {eng},

number = {4},

pages = {525-543},

publisher = {EDP-Sciences},

title = {A CAT algorithm for the exhaustive generation of ice piles},

url = {http://eudml.org/doc/246010},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Massazza, Paolo

AU - Radicioni, Roberto

TI - A CAT algorithm for the exhaustive generation of ice piles

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2010

PB - EDP-Sciences

VL - 44

IS - 4

SP - 525

EP - 543

AB - 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($\sqrt{n}$).

LA - eng

KW - sand pile model; ice pile model; integer partitions; exhaustive generation; CAT algorithms; discrete dynamical systems

UR - http://eudml.org/doc/246010

ER -

## References

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