Polyhedral combinatorics of bisectors
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| Název: | Polyhedral combinatorics of bisectors |
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| Autoři: | Jal, Aryaman, Jochemko, Katharina |
| Zdroj: | Advances in Geometry. 25(2):147-174 |
| Témata: | Polyhedral norm, bisector, polyhedral combinatorics, Wasserstein distance |
| Popis: | For any polyhedral norm, the bisector of two points is a polyhedral complex. We study combinatorial aspects of this complex. We investigate the sensitivity of the presence of labelled maximal cells in the bisector relative to the position of the two points. We thereby extend work of Criado, Joswig and Santos (2022) who showed that for the tropical distance function the presence of maximal cells is encoded by a polyhedral fan, the bisection fan. We initiate the study of bisection cones and bisection fans with respect to arbitrary polyhedral norms. In particular, we show that the bisection fan always exists for polyhedral norms in two dimensions. Furthermore, we determine the bisection fan of the & ell;1-norm and the & ell;infinity-norm as well as the discrete Wasserstein distance in arbitrary dimensions. Intricate combinatorial structures, such as the resonance arrangement, make their appearance. We apply our results to obtain bounds on the combinatorial complexity of the bisectors. |
| Popis souboru: | |
| Přístupová URL adresa: | https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-366151 https://doi.org/10.1515/advgeom-2025-0003 |
| Databáze: | SwePub |
Nájsť tento článok vo Web of Science | Abstrakt: | For any polyhedral norm, the bisector of two points is a polyhedral complex. We study combinatorial aspects of this complex. We investigate the sensitivity of the presence of labelled maximal cells in the bisector relative to the position of the two points. We thereby extend work of Criado, Joswig and Santos (2022) who showed that for the tropical distance function the presence of maximal cells is encoded by a polyhedral fan, the bisection fan. We initiate the study of bisection cones and bisection fans with respect to arbitrary polyhedral norms. In particular, we show that the bisection fan always exists for polyhedral norms in two dimensions. Furthermore, we determine the bisection fan of the & ell;1-norm and the & ell;infinity-norm as well as the discrete Wasserstein distance in arbitrary dimensions. Intricate combinatorial structures, such as the resonance arrangement, make their appearance. We apply our results to obtain bounds on the combinatorial complexity of the bisectors. |
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| ISSN: | 1615715X 16157168 |
| DOI: | 10.1515/advgeom-2025-0003 |