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The dimension of the divisibility order

Thu
11
Nov
Time Thursday 11 November, 2021 at 14:15 - 15:15
Place MA356

The Dushnik-Miller dimension of a partially-ordered set 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)2 (log log n)-Θ(1) as n goes to infinity. We will also see similar results when for variant notions of dimension and when the divisibility order taken over various other sets of integers.

Based on joint work with David Lewis and also with Leo Versteegen.

Event type: Seminar

Speaker: Victor Souza, University of Cambridge

Contact
Maryam Sharifzadeh
Read about Maryam Sharifzadeh