2016/10/06 by Enrique Navarrete, Navarrete, Enrique · 2 citations
Computer Science · Mathematics · #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1610.01987
arxiv created 2016/10/06 · openalex publication_date 2016/10/06 · arxiv updated 2016/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we count linear arrangements that avoid certain patterns and show their connection to the derangement numbers. We discuss the sequence Dn, which counts linear arrangements that avoid patterns 12, 23, ..., (n-1)n, n1, and show that this sequence almost follows the derangement sequence itself since the number of its odd terms is one more than the derangement numbers while the number of its even terms is one less. We also express the derangement numbers in terms of these and other arrangements.