We give factorizations for weighted spanning tree enumerators of Cartesian products of complete graphs, keeping track of fine weights related to degree sequences and edge directions. Our methods combine Kirchhoff's Matrix-Tree Theorem with the technique of identification of factors.
Bibliographical noteFunding Information:
$J.L.M. was supported by NSF Postdoctoral F ellowship. V.R. was supported by NSF Grant DMS-9877047. E-mail addresses: firstname.lastname@example.org (J.L. Martin), email@example.com (V. Reiner).
- Graph Laplacian
- Matrix-tree theorem
- Spanning tree