Combinatorics and Number Theory of Counting Sequences is an introduction to the theory
of finite set partitions and to the enumeration of cycle decompositions of permutations. The …

We introduce probabilistic Stirling numbers of the first kind s Y (n, k) associated with a
complex-valued random variable Y satisfying appropriate integrability conditions, thus …

Random structure plays an important role in the composition of compounds, and topological
index is an important index to measure indirectly the properties of compounds. The Zagreb …

A sequence $ s (n) $ of integers is MC-finite if for every $ m\in\mathbb {N}^+ $ the sequence
$ s^ m (n)= s (n)\bmod {m} $ is ultimately periodic. We discuss various ways of proving and …

In this paper, we introduce a new generalization of Bell numbers, the s-associated r-Dowling
numbers by combining two investigational directions. Here, r distinguished elements have to …

In this paper, we consider ordered set partitions obtained by imposing conditions on the size
of the lists, and such that the first $ r $ elements are in distinct blocks, respectively. We …

The determinant Hosoya triangle, is a triangular array where the entries are the
determinants of two-by-two Fibonacci matrices. The determinant Hosoya triangle mod 2 …

We introduce the $ B $-Stirling numbers of the first and second kind, which are the
coefficients of the potential polynomials when we express them in terms of the monomials …

arxiv:2303.11903v2 [math.CO] 31 Dec 2023 Page 1 arxiv:2303.11903v2 [math.CO] 31 Dec
2023 COUNTING FINITE TOPOLOGIES E. FISCHER AND JA MAKOWSKY Abstract. A finite …

We give explicit upper and lower bounds for a large subset of Comtet numbers s α (n, m) of
the first kind, including the r-Stirling numbers of the first kind, among others. In many …