$q$-Rationals and Finite Schubert Varieties
The classical $q$-analogue of the integers was recently generalized by Morier-Genoud and Ovsienko to give $q$-analogues of rational numbers. Some combinatorial interpretations are already known, namely as the rank generating functions for certain partially ordered sets. We give a new interpretation,...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.446/ |
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| Summary: | The classical $q$-analogue of the integers was recently generalized by Morier-Genoud and Ovsienko to give $q$-analogues of rational numbers. Some combinatorial interpretations are already known, namely as the rank generating functions for certain partially ordered sets. We give a new interpretation, showing that the numerators of $q$-rationals count the sizes of certain varieties over finite fields, which are unions of open Schubert cells in some Grassmannian. |
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| ISSN: | 1778-3569 |