Back to Search
Start Over
On [formula omitted]-neighborly reorientations of oriented matroids.
- Source :
-
European Journal of Combinatorics . May2024, Vol. 118, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- We study the existence and the number of k -neighborly reorientations of an oriented matroid. This leads to k -variants of McMullen's problem and Roudneff's conjecture, the case k = 1 being the original statements. Adding to results of Larman and García-Colín, we provide new bounds on k -McMullen's problem and prove the conjecture for several ranks and k by computer. Further, we show that k -Roudneff's conjecture for fixed rank and k reduces to a finite case analysis. As a consequence we prove the conjecture for odd rank r and k = r − 1 2 as well as for rank 6 and k = 2 with the aid of the computer. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATROIDS
*LOGICAL prediction
*NUMBER theory
Subjects
Details
- Language :
- English
- ISSN :
- 01956698
- Volume :
- 118
- Database :
- Academic Search Index
- Journal :
- European Journal of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 176150412
- Full Text :
- https://doi.org/10.1016/j.ejc.2024.103938