Minor-closed classes of binary functions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909378066513920 |
|---|---|
| author | Jones, Benjamin R. |
| author_facet | Jones, Benjamin R. |
| contents | Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and contraction. We give the excluded minor characterisations for the classes of binary functions with well defined minors, and those with an associated rank function. Within these classes, we also characterise the classes of binary functions corresponding to polymatroids, matroids and binary matroids by their excluded minors. This gives a new proof of Tutte's excluded minor characterisation of binary matroids in the more generalised space of binary functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_01320 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Minor-closed classes of binary functions Jones, Benjamin R. Combinatorics 05B35 (Primary) 15A03, 05C83(Secondary) Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and contraction. We give the excluded minor characterisations for the classes of binary functions with well defined minors, and those with an associated rank function. Within these classes, we also characterise the classes of binary functions corresponding to polymatroids, matroids and binary matroids by their excluded minors. This gives a new proof of Tutte's excluded minor characterisation of binary matroids in the more generalised space of binary functions. |
| title | Minor-closed classes of binary functions |
| topic | Combinatorics 05B35 (Primary) 15A03, 05C83(Secondary) |
| url | https://arxiv.org/abs/2102.01320 |