Separable d-Permutations and Guillotine Partitions |
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Authors: | Andrei Asinowski Toufik Mansour |
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Institution: | (2) Department of Computer Science, University of Texas at Dallas, Richardson, TX, USA;(3) Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USA; |
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Abstract: | We characterize separable multidimensional permutations in terms of forbidden patterns and enumerate them by means of generating
function, recursive formula, and explicit formula. We find a connection between multidimensional permutations and guillotine
partitions of a box. In particular, a bijection between separable d-dimensional permutations and guillotine partitions of a 2
d-1-dimensional box is constructed. We also study enumerating problems related to guillotine partitions under certain restrictions
revealing connections to other combinatorial structures. This allows us to obtain several results on patterns in permutations. |
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Keywords: | |
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