Enumeration of a dual set of Stirling permutations by their alternating runs

Abstract

In this paper, we count a dual set of Stirling permutations by the number of alternating runs. Properties of the generating functions, including recurrence relations, grammatical interpretations and convolution formulas are studied.

arXiv comment8 pages

References in corpus (2)

• The 1/k-Eulerian polynomials and k-Stirling permutations
• Stirling permutations, cycle structures of permutations and perfect matchings

Cited by in corpus (4)

• An asymptotic distribution theory for Eulerian recurrences with applications
• The ascent-plateau statistics on Stirling permutations
• The alternating run polynomials of permutations
• Stability of combinatorial polynomials and its applications