Let S[i, j] denote the q-Stirling numbers of the second kind. We show that the determinant of the matrix (S[s + i + j, s + j])0≤i,j≤n is given by the product q3(s+n+1)-3(s)·[s]0 · [s + 1]1 ⋯ [s + n]n. We give two proofs of this result, one bijective and one based upon factoring the matrix. We also prove an identity due to Cigler that expresses the Hankel determinant of q-exponential polynomials as a product. Lastly, a two variable version of a theorem of Sylvester and an application are presented.
|Number of pages||13|
|Journal||Advances in Applied Mathematics|
|State||Published - Nov 2003|
Bibliographical noteFunding Information:
The author thanks Margaret Readdy for comments on an earlier version of this paper. The author was partially supported by National Science Foundation grant 0200624.
ASJC Scopus subject areas
- Applied Mathematics