We introduce multivariable q-analogues of the determinant and show a sufficient condition for an interval of the symmetric group to have a symmetric chain decomposition in the Bruhat order by using the expansion formulas.
"q-Analogues of Determinants and Symmetric Chain Decompositions." Tokyo J. Math. 16 (2) 311 - 320, December 1993. https://doi.org/10.3836/tjm/1270128486