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The dimension of the divisibility order

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  • UserVictor Souza (Cambridge)
  • ClockThursday 25 November 2021, 14:30-15:30
  • HouseMR12.

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The Dushnik-Miller dimension of a poset P is the smallest d such that one can embed P into a product of d linear orders. We prove that the dimension of the divisibility order on the interval {1,...,n} is equal to (log n)\sup 2 (log log n)\sup{-Theta(1)} as n goes to infinity. We will also give similar results for variant notions of dimension and when the divisibility order is taken over various other sets of integers. Based on joint work with David Lewis and with Leo Versteegen.

This talk is part of the Combinatorics Seminar series.

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