Abstract
An involution on [n] = {1, 2,…, n} is a permutation π 1 π 2… πn on [n] such that π πi = i for all i ∈ [n]. Let π = π 1 π 2 n be any involution on [n]. We say that i is a covered fixed point of π if π i = i and there exists a, b such that 1 ≤ a < i < b ≤ n and π a = b. We say that ab is a covered arc of π if there exists c, d such that 1 ≤ c < a < b < d ≤ n, π a = b, and π c = d. In this paper, we study the generating function for the number of involutions on [n] according to the number of covered fixed points/covered arcs.
Original language | English |
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Pages (from-to) | 2625-2635 |
Number of pages | 11 |
Journal | Quaestiones Mathematicae |
Volume | 46 |
Issue number | 12 |
DOIs | |
State | Published - 2023 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2023 NISC (Pty) Ltd.
Keywords
- covered arcs
- covered fixed points
- Lined patterns
ASJC Scopus subject areas
- Mathematics (miscellaneous)