Pascal Eigenspaces and Invariant Sequences of the First or Second Kind

2017/06/06 by Ik-Pyo Kim, Kim, Ik-Pyo, Michael J. Tsatsomeros +1
Mathematics · Physics and Astronomy · #11B39 #11B65 #15B18 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1706.01573

openalex publication_date 2017/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An infinite real sequence \a_n\ is called an invariant sequence of the first (resp., second) kind if a_n=∑_k=0ⁿ n \choose k (-1)^k a_k (resp., a_n=∑_k=n^∞ k \choose n (-1)^k a_k). We review and investigate invariant sequences of the first and second kinds, and study their relationships using similarities of Pascal-type matrices and their eigenspaces.

Citations

• Some Open Questions about Random Walks, Involutions, Limiting Distributions, and Generating Functions

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