2026/07/22 by Abdelghani Mehdaoui
#math.CO
In this paper, we introduce the (r,d)-Stirling numbers of the second kind, a new generalization of the r-Stirling numbers obtained by imposing a distance restriction: for any two elements i and j within the same subset, we require that |i-j|>d. We establish recurrence relations, an explicit formula, ordinary and exponential generating functions, a reduction identity connecting these numbers to the standard r-Stirling numbers, and several combinatorial identities.