Comptes Rendus
Algèbre, Combinatoire
q-Rationals and Finite Schubert Varieties
Nicholas Ovenhouse1
1 Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven CT, USA
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 807-818.

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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Révisé le :
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DOI : 10.5802/crmath.446
Classification : 05A15, 05A17
Nicholas Ovenhouse 1

1 Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven CT, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     year = {2023},
     doi = {10.5802/crmath.446},
     language = {en},
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Nicholas Ovenhouse. $q$-Rationals and Finite Schubert Varieties. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 807-818. doi : 10.5802/crmath.446. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.446/

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