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arXiv · 2401.12969

Monadic transductions and definable classes of matroids

Susan Jowett·Dillon Mayhew·Songbao Mo·Christopher Tuffley
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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.

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Susan Jowett, Dillon Mayhew, Songbao Mo, Christopher Tuffley. 2024-01-23. Monadic transductions and definable classes of matroids. https://arxiv.org/abs/2401.12969

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