Finiteness of rank for Grassmann convexity
The Grassmann convexity conjecture, formulated in [8], gives a conjectural formula for the maximal total number of real zeroes of the consecutive Wronskians of an arbitrary fundamental solution to a disconjugate linear ordinary differential equation with real time. The conjecture can be reformulated...
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| Language: | English |
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Académie des sciences
2023-02-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.343/ |
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| author | Saldanha, Nicolau Shapiro, Boris Shapiro, Michael |
| author_facet | Saldanha, Nicolau Shapiro, Boris Shapiro, Michael |
| author_sort | Saldanha, Nicolau |
| collection | DOAJ |
| description | The Grassmann convexity conjecture, formulated in [8], gives a conjectural formula for the maximal total number of real zeroes of the consecutive Wronskians of an arbitrary fundamental solution to a disconjugate linear ordinary differential equation with real time. The conjecture can be reformulated in terms of convex curves in the nilpotent lower triangular group. The formula has already been shown to be a correct lower bound and to give a correct upper bound in several small dimensional cases. In this paper we obtain a general explicit upper bound. |
| format | Article |
| id | doaj-art-9919d9b02e2d4acca3fc06ac3d9057f6 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-9919d9b02e2d4acca3fc06ac3d9057f62025-02-07T11:06:36ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-02-01361G244545110.5802/crmath.34310.5802/crmath.343Finiteness of rank for Grassmann convexitySaldanha, Nicolau0Shapiro, Boris1Shapiro, Michael2Departamento de Matemática, PUC-Rio, R. Mq. de S. Vicente 225, Rio de Janeiro, RJ 22451-900, BrazilDepartment of Mathematics, Stockholm University, SE-106 91, Stockholm, SwedenDepartment of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA; National Research University Higher School of Economics, Moscow, RussiaThe Grassmann convexity conjecture, formulated in [8], gives a conjectural formula for the maximal total number of real zeroes of the consecutive Wronskians of an arbitrary fundamental solution to a disconjugate linear ordinary differential equation with real time. The conjecture can be reformulated in terms of convex curves in the nilpotent lower triangular group. The formula has already been shown to be a correct lower bound and to give a correct upper bound in several small dimensional cases. In this paper we obtain a general explicit upper bound.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.343/ |
| spellingShingle | Saldanha, Nicolau Shapiro, Boris Shapiro, Michael Finiteness of rank for Grassmann convexity Comptes Rendus. Mathématique |
| title | Finiteness of rank for Grassmann convexity |
| title_full | Finiteness of rank for Grassmann convexity |
| title_fullStr | Finiteness of rank for Grassmann convexity |
| title_full_unstemmed | Finiteness of rank for Grassmann convexity |
| title_short | Finiteness of rank for Grassmann convexity |
| title_sort | finiteness of rank for grassmann convexity |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.343/ |
| work_keys_str_mv | AT saldanhanicolau finitenessofrankforgrassmannconvexity AT shapiroboris finitenessofrankforgrassmannconvexity AT shapiromichael finitenessofrankforgrassmannconvexity |