Eulerian Polynomials, Stirling Permutations of the Second Kind and Perfect Matchings

  • Shi-Mei Ma
  • Yeong-Nan Yeh
Keywords: Eulerian polynomials, Stirling permutations of the second kind, Stirling derangements


In this paper, we introduce Stirling permutations of the second kind. In particular, we count Stirling permutations of the second kind by their cycle ascent plateaus, fixed points and cycles. Moreover, we get an expansion of the ordinary derangement polynomials in terms of the Stirling derangement polynomials. Finally, we present constructive proofs of a kind of combinatorial expansions of the Eulerian polynomials of types $A$ and $B$.

Author Biographies

Shi-Mei Ma, Northeastern University at Qinhuangdao
School of Mathematics and Statistics
Yeong-Nan Yeh, Academia Sinica
Institute of Mathematics
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