The 1/k-Eulerian polynomials and k-Stirling permutations

Shi Mei Ma, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


In a recent work of Savage and Viswanathan (2012), during studies of the set of n-dimensional k-inversion sequences, the so-called 1/k-Eulerian polynomials have been introduced, which are given as generating polynomials of the number of ascents in such inversion sequences. In this paper, we discover that the 1/k-polynomials are also generating polynomials of the number of the longest ascent plateaus of k-Stirling permutations. Moreover, we also introduce the dual set of Stirling permutations.

Original languageEnglish
Pages (from-to)1468-1472
Number of pages5
JournalDiscrete Mathematics
Issue number8
StatePublished - 6 Aug 2015

Bibliographical note

Funding Information:
The first author was supported by NSFC ( 11401083 ), the Fundamental Research Funds for the Central Universities ( N130423010 ), the Research Foundation for Science and Technology Pillar Program of Northeastern University at Qinhuangdao (XNK201303) and the Natural Science Foundation of Hebei Province ( A2013501070 ). The authors thank the referee for many detailed suggestions leading to a substantial improvement of this paper.

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.


  • 1 / k-Eulerian polynomials
  • Alternating runs
  • Longest ascent plateaus
  • k-Stirling permutations

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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