Dually weighted Stirling-type sequences
Combinatorics
2014-07-29 v3
Abstract
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 -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.
Cite
@article{arxiv.1302.4694,
title = {Dually weighted Stirling-type sequences},
author = {Roberto B. Corcino and Ken Joffaniel M. Gonzales and Manuel Joseph C. Loquias and Evelyn L. Tan},
journal= {arXiv preprint arXiv:1302.4694},
year = {2014}
}
Comments
13 pages, 1 figure, submitted to European J. Combin