Partial Bell Polynomials, Falling and Rising Factorials, Stirling Numbers, and Combinatorial Identities  

作　　者：Siqintuya Jin Bai-Ni Guo Feng Qi 

机构地区：[1]College of Mathematics and Physics,Inner Mongolia Minzu University,Tongliao,028043,China [2]School of Mathematics and Informatics,Henan Polytechnic University,Jiaozuo,454010,China [3]School of Mathematical Sciences,Tiangong University,Tianjin,300387,China

出　　处：《Computer Modeling in Engineering & Sciences》2022年第9期781-799,共19页工程与科学中的计算机建模（英文）

基　　金：supported in part by the National Natural Science Foundation of China(Grant No.12061033);by the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grants No.NJZY20119);by the Natural Science Foundation of Inner Mongolia(Grant No.2019MS01007),China.

摘　　要：In the paper,the authors collect,discuss,and find out several connections,equivalences,closed-form formulas,and combinatorial identities concerning partial Bell polynomials,falling factorials,rising factorials,extended binomial coefficients,and the Stirling numbers of the first and second kinds.These results are new,interesting,important,useful,and applicable in combinatorial number theory.

关 键 词：Connection EQUIVALENCE closed-form formula combinatorial identity partial Bell polynomial falling factorial rising factorial binomial coefficient Stirling number of the first kind Stirling number of the second kind problem 

分 类 号：O17[理学—数学]