International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 96327, 10 pages

Combinatorial identities by way of Wilf's multigraph model

Theresa L. Friedman1 and Paul Klingsberg2

1Mesa State College, 1100 North Avenue, Grand Junction 81502, CO, USA
2Saint Joseph's University, 5600 City Avenue, Philadelphia 19131-1395, PA, USA

Received 4 February 2005; Revised 29 October 2006; Accepted 9 November 2006

Copyright © 2006 Theresa L. Friedman and Paul Klingsberg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For many families of combinatorial objects, a construction of Wilf (1977) allows the members of the family to be viewed as paths in a directed multigraph. Introducing a partition of these paths generates a number of known, but hitherto disparate, combinatorial identities. We include several examples.