Geodesic
Algèbre, Combinatoire
q-Rationals and Finite Schubert Varieties
Ovenhouse, Nicholas1
1 Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven CT, USA
Comptes Rendus. Mathématique, Tome 361 (2023) no. G4, pp. 807-818

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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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DOI : 10.5802/crmath.446
Classification : 05A15, 05A17

Ovenhouse, Nicholas 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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     journal = {Comptes Rendus. Math\'ematique},
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Ovenhouse, Nicholas. $q$-Rationals and Finite Schubert Varieties. Comptes Rendus. Mathématique, Tome 361 (2023) no. G4, pp. 807-818. doi: 10.5802/crmath.446

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