<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-Rationals and Finite Schubert Varieties

The classical q-analogue of the integers was recently generalized by Morier-Genoud and Ovsienko to give q-analogues rational numbers. Some combinatorial interpretations are already known, namely as rank generating functions for certain partially ordered sets. We a new interpretation, showing that numerators q-rationals count sizes varieties over finite fields, which unions open Schubert cells in some Grassmannian.