Monadic transductions and definable classes of matroids
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914649737265152 |
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| author | Jowett, Susan Mayhew, Dillon Mo, Songbao Tuffley, Christopher |
| author_facet | Jowett, Susan Mayhew, Dillon Mo, Songbao Tuffley, Christopher |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monadic transductions and definable classes of matroids Jowett, Susan Mayhew, Dillon Mo, Songbao Tuffley, Christopher Combinatorics 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. |
| title | Monadic transductions and definable classes of matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2401.12969 |