Separable d-permutations and guillotine partitions

Details Separable d-permutations and guillotine partitions Separable d-permutations and guillotine partitions

2008-03-24

arxiv.org/abs/0803.3414v1

Mathematics

Combinatorics

20 pages, 13 figures

Scientific paper

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 $d$-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 results on avoided patterns in permutations.

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