Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21286220211201Stirling number of the fourth kind and lucky partitions of a finite set2112191411510.22049/cco.2020.26895.1158ENJohanKokIndependent Mathematics Researcher, City of Tshwane0000-0003-0106-1676Joseph VargheseKureetharaDepartment of Mathematics, Christ University0000-0001-5030-3948Journal Article20200729The concept of Lucky <em>k</em>-polynomials and in particular Lucky <em>χ</em>-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky <em>k</em>- or Lucky <em>χ</em>-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.http://comb-opt.azaruniv.ac.ir/article_14115_627b858f0bf943ab54b52dab41740340.pdf