Abstract
Using dynamical systems and order theory, we give results about two kinds of combinatorial objects: generalized integer partitions and tilings of zonotopes. We show that these objects naturally have the (distributive) lattice structure. We also discuss the special case of linear integer partitions, for which other dynamical systems exist. These results give a better understanding of the behaviour of tilings of zonotopes with flips and dynamical systems involving partitions. A longer version of this paper, with full proofs, discussion and an application, is available at http://www.liafa.jussieu.fr/~latapy.
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Latapy, M. (2000). Generalized Integer Partitions, Tilings of Zonotopes and Lattices. In: Krob, D., Mikhalev, A.A., Mikhalev, A.V. (eds) Formal Power Series and Algebraic Combinatorics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04166-6_23
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DOI: https://doi.org/10.1007/978-3-662-04166-6_23
Publisher Name: Springer, Berlin, Heidelberg
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