A new kind of signed permutations in the view of context-free grammar
Zhibin Du, Hong Bian, Junran Lichen, Jean Yeh
article (Uluslararası, Hakemli) | Yazar(lar): Zhibin Du, Hong Bian, Junran Lichen, Jean Yeh | Yıl: 2027 | Dergi/Kurum: DISCRETE MATHEMATICS | İndeks: WOS.SCI | DOI: 10.1016/j.disc.2026.115396 | Anahtar Kelimeler: Signed permutations, Context-free grammar, Determinantal expressions, Asymptotic normality — Özet: A new ki
A new kind of signed permutations is proposed in this paper. Based on the standard permutation defined by {1, 2, ... , n}, we assign a sign (either positive or negative) to each number, including the boundary elements at both ends, the resulting permutation is called a signed permutation. Eight combinatorial statistics about ascents, descents, sign changes with respect to the signs are introduced. With the help of the context-free grammar theory, a series of combinatorial properties of such signed permutations are presented, mainly in the aspects of (homogeneous) gamma-positivity, (homogeneous) bi-gamma-positivity, determinantal expressions, P & oacute;lya-frequency, unimodal, log-concave, real-rooted, asymptotic normality. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.