Year: 2025
Type: article
Abstract: For a given function from a set to itself, we can define a directed graph called the functional graph, where the vertices are the elements of the set, and the edges are all the pairs of inputs and outputs for the function. In this paper, we consider functional graphs on [Formula: see text] with respect to polynomial functions. The main result describes the behavior of cycles in functional graphs on [Formula: see text] while [Formula: see text] is increasing, where [Formula: see text] is a prime number.
Author: Tadahisa Nara
Institution: Tokyo Information Design Professional University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416388489
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