arXiv subjects

Ik-Pyo Kim

Publications and source records attributed to Ik-Pyo Kim.

2 recordsLinked to original sources

arXiv2017

Inverse Relations in Shapiro's Open Questions

As an inverse relation, involution with an invariant sequence plays a key role in combinatorics and features prominently in some of Shapiro's open questions [L.W. Shapiro, Some open questions about random walks, involutions, limiting distributions and generating functions, Adv. Appl. Math. 27 (2001) 585-596]. In this paper, invariant sequences are used to provide answers to some of these questions about the Fibonacci matrix and Riordan involutions.

math.CO↗

arXiv2017

Pascal Eigenspaces and Invariant Sequences of the First or Second Kind

An infinite real sequence $\{a_n\}$ is called an invariant sequence of the first (resp., second) kind if $a_n=\sum_{k=0}^n {n \choose k} (-1)^k a_k$ (resp., $a_n=\sum_{k=n}^{\infty} {k \choose n} (-1)^k a_k$). 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.

math.CO↗