2024/03/08 by Yunseo Choi, Choi, Yunseo, Katelyn Gan +5
Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Advanced Combinatorial Mathematics #Advanced Algebra and Logic
paper · pdf · doi:10.48550/arxiv.2403.05113
Recently, Xia introduced a deterministic variation ϕσ of Defant and Kravitz's stack-sorting maps for set partitions and showed that any set partition p is sorted by ϕN(p)aba, where N(p) is the number of distinct alphabets in p. Xia then asked which set partitions p are not sorted by ϕabaN(p)-1. In this note, we prove that the minimal length of a set partition p that is not sorted by ϕabaN(p)-1 is 2N(p). Then we show that there is only one set partition of length 2N(p) and N(p) + 1 \choose 2 + 2N(p) \choose 2 set partitions of length 2N(p)+1 that are not sorted by ϕabaN(p)-1.