2004/11/02 by Kennan Shelton, Shelton, Kennan, Michael Siler +1
Computer Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Dynamics and Fractals #math.CO #math.GM #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0411052
13 pages, 4 figures
arxiv created 2004/11/02 · openalex publication_date 2004/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a set of coins arranged in a line, we remove heads-up coins one at a time and flip any adjacent coins after each removal. The coin-removal problem is to determine for which arrangements of coins it is possible to remove all of the coins. In this paper we consider a variation of the problem in which gaps created by removing coins are eliminated by pushing the coins together. We characterize the set of removable arrangements and show that this set forms a regular language. We use a finite automaton to find a recursive formula for the number of removable arrangements of different lengths.