Geodesic
The Bhargava greedoid as a Gaussian elimination greedoid
Darij Grinberg1
1University of Minnesota, Twin Cities
The electronic journal of combinatorics, Tome 31 (2024) no. 2
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Inspired by Manjul Bhargava's theory of generalized factorials, Grinberg and Petrov 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.
DOI : 10.37236/11222
Classification : 05B35, 12J25, 52B40
Mots-clés : greedy algorithm, Bhargava greedoid

Darij Grinberg  1

1 University of Minnesota, Twin Cities 
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Darij Grinberg. The Bhargava greedoid as a Gaussian elimination greedoid. The electronic journal of combinatorics, Tome 31 (2024) no. 2. doi: 10.37236/11222

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