2022/05/30 by Gi‐Sang Cheon, Tamás Forgács, Cheon, Gi-Sang +5 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #05A15 #05A40 #30C15 #30E15 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Coding theory and cryptography #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2205.15471
openalex publication_date 2022/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present combinatorial and analytical results concerning a Sheffer sequence with an exponential generating function of the form G(s,z)=e^czs+αz2+βz4, where α, β, c ∈ ℝ with β<0 and c≠ 0. We demonstrate that the zeros of all polynomials in such a Sheffer sequence are either real, or purely imaginary. Additionally, using the properties of Riordan matrices we show that our Sheffer sequence satisfies a three-term recurrence relation of order 4, and we also exhibit a connection between the coefficients of these Sheffer polynomials and the number of nodes with a a given label in certain marked generating trees.