@article{Kim2023, 
author = {Taekyun Kim and Dae San Kim and Jin-Woo Park},
title = {Degenerate    r-truncated Stirling numbers},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {25957-25965},
keywords = {degenerate r-associated Stirling numbers of the second kind, degenerate r-truncated Stirling numbers of the first kind, degenerate r-truncated Bell polynomials},
url = {https://www.sciopen.com/article/10.3934/math.20231322},
doi = {10.3934/math.20231322},
abstract = {For any positive integer    r, the    r-truncated (or    r-associated) Stirling number of the second kind        S          2              (      r      )        (  n  ,  k  ) enumerates the number of partitions of the set    {  1  ,  2  ,  3  ,  …  ,  n  } into    k non-empty disjoint subsets, such that each subset contains at least    r elements. We introduce the degenerate    r-truncated Stirling numbers of the second kind and of the first kind. They are degenerate versions of the    r-truncated Stirling numbers of the second kind and of the first kind, and reduce to the degenerate Stirling numbers of the second kind and of the first kind for    r  =  1. Our aim is to derive recurrence relations for both of those numbers.}
}