Abstract
The limit expression, denoted by ����,��(��, ��) was evaluated completely that yields an explicit formula in elementary symmetric function form. The limit ����,��(��, ��) has possessed some necessary properties like recurrence relations, generating functions, orthogonality relation, inverse relation and matrix factorization. It has been identified that the numbers ����,��(��, ��) are certain generalization of Gould-Hopper numbers, which are useful in biology and reliability theory. One can easily verify that these numbers are equivalent to the first kind r-Whitney numbers using their existing properties. In this present paper, a combinatorial meaning for r-Whitney numbers of the first kind in the context of (0, 1)-tableau is constructed using the explicit formula in symmetric function form. Moreover, some convolution-type formulas are derived that, consequently, yield LU-factorization of the matrix whose entries are the first kind r-Whitney numbers.,
Recommended Citation
Corcino, Roberto B. and Corcino, Cristina B.
(2015)
"On the First Kind r-Whitney Numbers and the Combinatorics of 0-1 Tableaux,"
CNU Journal of Higher Education: Vol. 9:
Iss.
1, Article 11.
DOI: https://doi.org/10.70997/2546-1796.1121
Available at:
https://jhe.researchcommons.org/journal/vol9/iss1/11