On a Question of Gowers on Clique Differences
Ryan Alweiss
TL;DR
This paper addresses a question by Gowers regarding clique differences in chains, providing a definitive answer that impacts the approach to the polynomial density Hales-Jewett theorem for binary alphabets.
Contribution
It resolves Gowers' 2009 question, ruling out Sperner-type proofs for the polynomial density Hales-Jewett theorem in the binary case.
Findings
Gowers' question on clique differences is answered.
Sperner-type proofs are ruled out for the binary case.
Advances understanding of combinatorial structures in chains.
Abstract
We solve a question of Gowers from 2009 on clique differences in chains, thus ruling out any Sperner-type proof of the polynomial density Hales-Jewett theorem for alphabets of size 2.
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Taxonomy
TopicsLimits and Structures in Graph Theory · semigroups and automata theory · graph theory and CDMA systems