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Preprint
The Bhargava greedoid as a Gaussian elimination greedoid
arXiv (Cornell University)
15 Jan 2020
Abstract
Inspired by Manjul Bhargava's theory of generalized factorials, Fedor Petrov
and the author have defined the "Bhargava greedoid" -- a greedoid (a
matroid-like set system on a finite set) assigned to any "ultra triple" (a
somewhat extended variant of a finite ultrametric space). Here we show that the
Bhargava greedoid of a finite ultra triple is always a "Gaussian elimination
greedoid" over any sufficiently large (e.g., infinite) field; this is a
greedoid analogue of a representable matroid. We find necessary and sufficient
conditions on the size of the field to ensure this.
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Details
- Title
- The Bhargava greedoid as a Gaussian elimination greedoid
- Creators
- Darij Grinberg
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862369204721