\(\lambda\)-Euler's difference table for colored permutations
Summary: Motivated by the \(\lambda\)-Euler's difference table of \textit{N. Eriksen} et al. [Electron. J. Comb. 16, No. 1, Research Paper R32, 19 p. (2009; Zbl 1181.05003)] and colored Euler's difference table of \textit{H. L. M. Faliharimalala} and \textit{J. Zeng} [Electron. J. Comb. 15, No. 1, Research Paper R65, 22 p. (2008; Zbl 1181.05013)], we study the \(\lambda\)-analogue of colored Euler's difference table and generalize their results. We generalize the number of permutations with \(k\)-excedances studied by \textit{J. Liese} and \textit{J. Remmel} [PU.M.A., Pure Math. Appl. 21, No. 2, 285--320 (2010; Zbl 1265.05017)] in colored permutations. We also extend \textit{C. Wang} et al.'s [Discrete Math. 340, No. 7, 1681--1692 (2017; Zbl 1415.05007)] recent results about \(r\)-derangements by relating with the sequences arising from the difference table.
scientific article; zbMATH DE number 6983023
scientific article