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A Relationship between the Partial Bell Polynomials and Alternating Run Polynomials
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, China
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, China
- 1 School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, China
- 2 School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, China
Open Journal of Discrete Mathematics·Volume 13 (2023)·Pages 49–54·Published 18 April 2023·DOI10.4236/ojdm.2023.132005
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Abstract
In this note, we first derive an exponential generating function of the alternating run polynomials. We then deduce an explicit formula of the alternating run polynomials in terms of the partial Bell polynomials.
KeywordsAlternating Run PolynomialsBell PolynomialsPermutations
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