%0 Journal Article %T Generalized Legendre-Stirling Numbers %A K. C. Garrett %A Kendra Killpatrick %J Open Journal of Discrete Mathematics %P 109-114 %@ 2161-7643 %D 2014 %I Scientific Research Publishing %R 10.4236/ojdm.2014.44014 %X The Legendre-Stirling numbers were discovered by Everitt, Littlejohn and Wellman in 2002 in a study of the spectral theory of powers of the classical second-order Legendre differential operator. In 2008, Andrews and Littlejohn gave a combinatorial interpretation of these numbers in terms of set partitions. In 2012, Mongelli noticed that both the Jacobi-Stirling and the Legendre-Stirling numbers are in fact specializations of certain elementary and complete symmetric functions and used this observation to give a combinatorial interpretation for the generalized Legendre-Stirling numbers. In this paper we provide a second combinatorial interpretation for the generalized Legendre-Stirling numbers which more directly generalizes the definition of Andrews and Littlejohn and give a combinatorial bijection between our interpretation and the Mongelli interpretation. We then utilize our interpretation to prove a number of new identities for the generalized Legendre-Stirling numbers. %K Stirling Numbers %K Legendre-Stirling Numbers %K Set Partitions %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50593