Equipartitions beyond primes and prime powers

by Alena Zhukova (SpBGU)

Monday 15 Mar 2021, 11:15 → 13:15 Europe/Moscow

120(413) (14 line)

We discuss a number of related equipartition problems. Their common feature is that if the number of tiles is a prime power, the proof explores some topological facts that  are no longer true for the general case. 

 

We are mainly interested in going beyond prime powers.

 

 (1)  Nandakumar & Ramana Rao conjectured that  every convex polygon P in the plane
can be partitioned into any prescribed number n of convex pieces that have equal area and equal
perimeter.

 

First, we discuss the proof for n=p^a    (based  on  https://arxiv.org/pdf/1202.5504.pdf )

And then the proof for arbitrary n (https://arxiv.org/pdf/1804.03057.pdf)

 

(2) Equipartition (related to some evaluating function)  of a segment  (https://arxiv.org/pdf/2009.09862.pdf)