Vector weighted Stirling numbers and an application in graph theory - Fahimeh Esmaeeli; Ahmad Erfanian; Madjid Mirzavaziri (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2021)
We introduce vector weighted Stirling numbers, which are a generalization of ordinary Stirling numbers and restricted Stirling numbers. Some relations between vector weighted Stirling numbers and ordinary Stirling numbers and some of their applications are stated. Moreover, as an application of vector weighted Stirling numbers of the second kind in graph theory, we compute the number of maximal independent sets of different sizes in k-intersection graphs.