Kneser's Theorem and the Cauchy–Davenport Theorem

Abstract

We formalise Kneser's Theorem in combinatorics following the proof from the 2014 paper A short proof of Kneser’s addition theorem for abelian groups by Matt DeVos. We also show a strict version of Kneser's Theorem as well as the Cauchy–Davenport Theorem as a corollary of Kneser's Theorem.

License

BSD License

Topics

Mathematics/Combinatorics

Related publications

DeVos, M. (2014). A Short Proof of Kneser’s Addition Theorem for Abelian Groups. Combinatorial and Additive Number Theory, 39–41. https://doi.org/10.1007/978-1-4939-1601-6_3
Nathanson, Melvyn B, Additive Number Theory: Inverse Problems and the Geometry of Sumsets, Springer-Verlag, 1996, vol. 165, Graduate Texts in Mathematics, isbn 978-0-387-94655-9
Ruzsa, Imre Z., Sumsets and Structure, Course notes, 2008, available on https://www.math.cmu.edu/users/af1p/Teaching/AdditiveCombinatorics/Additive-Combinatorics.pdf

Session Kneser_Cauchy_Davenport

Kneser_Cauchy_Davenport_preliminaries
Kneser_Cauchy_Davenport_main_proofs

Depends on

A Case Study in Basic Algebra
The Plünnecke-Ruzsa Inequality