Determinants in plane partition enumeration
The determinant \(\text{det}\left(\delta_{ij}+ \left(\begin{smallmatrix} x+i+j\\ j\end{smallmatrix}\right)\right)\), \(0\leq i\), \(j\leq n-1\), arose in the enumeration of a certain set of plane partitions and was evaluated by \textit{W. H. Mills}, \textit{D. P. Robbins} and \textit{H. Rumsey} [Discrete Math. 67, 43-55 (1987; Zbl 0656.05006)]. The authors now give a new more concise proof of the result. Another proof can be obtained via the recent computer-aided approach of \textit{M. Petkovšek} and \textit{H. S. Wilf} [Electron. J. Comb. 3, No. 2, Paper R19, 3p. (1996; Zbl 0851.05005)].
scientific article; zbMATH DE number 1199949