2022/08/08 by Thackeray, Henry Robert
#05A19 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2208.04395
For positive integers n and k such that k is at most n, we find an explicit one-to-one correspondence between the following two sets: the set of words consisting of k Rs, k Us, and n - k Ds, where the first letter of the word is not D; and the set of subgraphs H of a cycle of length 2n (where that cycle has differently labelled vertices) such that H has n edges and k connected components. This solves a problem of Thomas Selig from the 29th British Combinatorial Conference held at Lancaster University in July 2022.