컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0219 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-22) Enumerative Combinatorics (SS-22) |
| 발표시간(Time) | 20th-D-14:00 -- 14:30 |
| 영문제목 (Title(Eng.)) |
Bijections on \( (2341,3241,2431) \)-avoiding permutations and related objects |
| 저자(Author(s)) |
JiSun Huh1, Sangwook Kim2, Seunghyun Seo3, Heesung Shin4 Ajou University1, Chonnam National University2, Kangwon National University3, Inha University4 |
| 초록본문(Abstract) | The number of permutations avoiding three patterns \( 2341, 3241 \), and \( 2431\) is known to be the same as the number of inversion sequences avoiding two patterns \( 101 \) and \( 102 \). This sequence also counts the number of Schr\"{o}der path without triple descents, restricted bicolored Dyck paths, \( (101,021) \)-avoiding inversion sequences, and weighted ordered trees. In this talk, we introduce \emph{\( F \)-paths} which are lattice paths with steps in the set \[ F := \{ (a, b) : a \geq 1, b \leq 1 \} \cup \{ (0,1) \} \] that never go below the line \( y=x \). We construct a bijection from the \( (2341,3241,2431) \)-avoiding permutations to the \( F \)-paths. Moreover, we provide three statistics for each of the objects and count the number of each objects with respect to these statistics. |
| 분류기호 (MSC number(s)) |
Primary 05A19; Secondary 05A05, 05A15 |
| 키워드(Keyword(s)) | Permutations, inversion sequences, pattern avoidance, lattice paths |
| 강연 형태 (Language of Session (Talk)) |
Korean |