Hales-Jewett type configurations in small sets
Combinatorics
2021-12-03 v2
Abstract
In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. Their work was completely algebraic in nature, where they have used the algebra of Stone-Cech compactification of discrete semigroup. They have proved the existence of those configurations in piecewise syndetic sets, which is a Ramsey theoretic rich set. In our work we will show those forms are still present in very small but Ramsey theoretic sets, (like J-set, C-set) and our proof is purely elementary in nature.
Cite
@article{arxiv.2009.00772,
title = {Hales-Jewett type configurations in small sets},
author = {Aninda Chakraborty and Sayan Goswami},
journal= {arXiv preprint arXiv:2009.00772},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:1807.01485 by other authors