Geodesic
Strong greedoid structure of \(r\)-removed \(P\)-orderings
Dmitrii Krachun1 ; Rozalina Mirgalimova2
1Princeton University
2Saint Petersburg State University
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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Inspired by the notion of $r$-removed $P$-orderings introduced in the setting of Dedekind domains by Bhargava, we generalize it to the framework of arbitrary ultrametric spaces. We show that sets of maximal "$r$-removed perimeter" can be constructed by a greedy algorithm and form a strong greedoid. This gives a simplified proof of several theorems previously obtained by Bhargava, as well as generalises some results of Grinberg and Petrov who considered the case $r=0$ corresponding, in turn, to simple $P$-orderings.
DOI : 10.37236/12403
Classification : 13F05, 05B35
Mots-clés : \(P\)-adic valuation, ultra triple, greedy \(r\)-removed \(m\)-permutations, strong greedoid

Dmitrii Krachun  1   ; Rozalina Mirgalimova  2

1 Princeton University
2 Saint Petersburg State University 
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     title = {Strong greedoid structure of \(r\)-removed {\(P\)-orderings}},
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Dmitrii Krachun; Rozalina Mirgalimova. Strong greedoid structure of \(r\)-removed \(P\)-orderings. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12403

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