Random Linear Extensions of Grids

Details Random Linear Extensions of Grids Random Linear Extensions of Grids

2006-02-22

arxiv.org/abs/math/0602509v1

Mathematics

Combinatorics

13 pages, no figures

Scientific paper

A grid poset -- or grid for short -- is a product of chains. We ask, what does a random linear extension of a grid look like? In particular, we show that the average "jump number," i.e., the number of times that two consecutive elements in a linear extension are incomparable in the poset, is close to its maximum possible value. The techniques employed rely on entropy arguments. We finish with several interesting questions about this wide-open area.

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