Electronic Journal of Combinatorics
By counting flags in finite vector spaces, we obtain a q-multinomial analog of a recursion for q-binomial coefficients proved by Nijenhuis, Solow, and Wilf. We use the identity to give a combinatorial proof of a known recurrence for the generalized Galois numbers.
Vinroot, C. R. (2012). An enumeration of flags in finite vector spaces. the electronic journal of combinatorics, 19(3), 5.