2013/02/28 by Roberto B. Corcino, Ken Joffaniel M. Gonzales, Manuel Joseph C. Loquias +1
Mathematics · #math.CO #msc:05A10 #msc:11B73 #msc:11B65
paper · pdf · doi:10.1016/j.ejc.2014.06.010
published as European J. Combin. 43 (2015) 55-67 · 13 pages, 1 figure, submitted to European J. Combin
arxiv created 2014/01/06 · arxiv updated 2014/07/29
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other sequences such as the p,q-binomial coefficients. Recurrence relations, generating functions, orthogonality relations, convolution formulas, and determinants of certain matrices involving the obtained sequences are derived. We also give combinatorial interpretations of certain cases in terms of colored partitions and permutations.