10:00 - 11:00, October 27, 2025 (Monday) Room 515, Cosmology Building, NTU
(臺灣大學次震宇宙館 515研討室)
Multiple Perspectives on Eulerian and Stirling Polynomials Chun-Chen Yeh (National Kaohsiung Normal University)
Abstract
In this talk, we explore Eulerian polynomials and Stirling permutations from several interrelated perspectives. Building upon the framework established in our earlier works—spanning differential equations, differential operators, and several combinatorial models—we further uncover the structural and algebraic connections linking these two central families.
For Stirling permutations, we introduce the concept of Stirling permutation codes, highlighting their effectiveness in encoding equidistribution phenomena and generating multivariate expansions. Moreover, by incorporating the theory of grammatical bases, we demonstrate how formal grammars provide a unified language for studying diverse families of polynomials, such as Eulerian, Narayana, and derivative polynomials.
Within this extended framework, we obtain a series of -positive and -positive expansions, establish interlacing and alternatingly increasing properties, and reveal new relationships among statistics on type A and B permutations, signed permutations, and Stirling structures.
