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We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the
ice pile model
a generalization of the
sand pile model
More precisely, for any fixed integer k, we show that
the negative lexicographic ordering naturally identifies a tree structure on the lattice
this lets us design an algorithm which generates all the ice piles of
in amortized time
and in space
In this work we study some probabilistic models for the random generation of words over a given alphabet
used in the literature in connection with pattern statistics.
Our goal is to compare models based on Markovian processes (where the occurrence of a symbol in a given position
only depends on a finite number of previous occurrences) and the stochastic models that
can generate a word of given length from a regular language under uniform distribution.
We present some results that show the differences between these two stochastic models and their
relationship with the rational probabilistic measures.
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