Given two partitions M and N, with $M\_i \leq N\_i$ for all $1\leq i\leq \max\{l(M),l(N)\}$. Is there a formula for the generating function: $$\sum\_{\lambda: M\_i\leq \lambda\_i\leq N\_i} q^{|\lambda|}$$ 


I remember seeing a determinant formula before, the elements of the determinant being q-binomial coefficients. But now I can't find it.



The number of partitions between two fixed partitions
Note on enumeration of partitions contained in a given shape


by Ira M. Gessel and Nicholas Loehr


link:
<http://www.sciencedirect.com/science/article/pii/S0024379509004819>


