Monadic transductions and definable classes of matroids
Combinatorics
2024-01-24 v1
Abstract
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a self-contained presentation of the theory of transductions for the monadic second-order language of matroids. This includes a proof of the matroid version of the Backwards Translation Theorem, which lifts any formula applied to the images of the transduction into a formula which we can apply to the pre-images. Applications include proofs that the class of lattice-path matroids and the class of spike-minors can be defined by sentences in monadic second-order logic.
Cite
@article{arxiv.2401.12969,
title = {Monadic transductions and definable classes of matroids},
author = {Susan Jowett and Dillon Mayhew and Songbao Mo and Christopher Tuffley},
journal= {arXiv preprint arXiv:2401.12969},
year = {2024}
}