Linz, William; Yan, Catherine Derangements on a Ferrers board. (English) Zbl 1325.05012 Discrete Math. Algorithms Appl. 7, No. 3, Article ID 1550036, 17 p. (2015). Summary: We study the derangement number on a Ferrers board \(B = (n \times n) - \lambda\) with respect to an initial permutation \(M\), that is, the number of permutations on \(B\) that share no common points with \(M\). We prove that the derangement number is independent of \(M\) if and only if \(\lambda\) is of rectangular shape. We characterize the initial permutations that give the minimal and maximal derangement numbers for a general Ferrers board, and present enumerative results when \(\lambda\) is a rectangle. MSC: 05A05 Permutations, words, matrices 05A18 Partitions of sets Keywords:derangement; Ferrers board PDFBibTeX XMLCite \textit{W. Linz} and \textit{C. Yan}, Discrete Math. Algorithms Appl. 7, No. 3, Article ID 1550036, 17 p. (2015; Zbl 1325.05012) Full Text: DOI References: [1] Armstrong D., Mem. Amer. Math. Soc. 202 pp x+159– (2009) [2] Brualdi R. A., Introductory Combinatorics (2010) · Zbl 0734.05001 [3] DOI: 10.1007/s00493-007-2297-2 · Zbl 1164.05002 · doi:10.1007/s00493-007-2297-2 [4] de Montmort P. R., Essay d’Analyse Sur Les Jeux de Hazard (1713) [5] DOI: 10.1215/S0012-7094-46-01324-5 · Zbl 0060.02903 · doi:10.1215/S0012-7094-46-01324-5 [6] DOI: 10.1016/j.laa.2010.07.030 · Zbl 1200.15003 · doi:10.1016/j.laa.2010.07.030 [7] DOI: 10.1017/CBO9780511735127 · Zbl 1133.60003 · doi:10.1017/CBO9780511735127 [8] DOI: 10.1007/978-0-387-76731-4 · Zbl 1207.92013 · doi:10.1007/978-0-387-76731-4 [9] DOI: 10.1017/CBO9780511805967 · doi:10.1017/CBO9780511805967 [10] DOI: 10.1016/j.aam.2013.06.001 · Zbl 1281.05045 · doi:10.1016/j.aam.2013.06.001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.