TY - JOUR
T1 - On Pattern-Avoiding Fishburn Permutations
AU - Gil, Juan B.
AU - Weiner, Michael D.
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - The class of permutations that avoid the bivincular pattern (231 , { 1 } , { 1 }) is known to be enumerated by the Fishburn numbers. In this paper, we call them Fishburn permutations and study their pattern avoidance. For classical patterns of size 3, we give a complete enumerative picture for regular and indecomposable Fishburn permutations. For patterns of size 4, we focus on a Wilf equivalence class of Fishburn permutations that are enumerated by the Catalan numbers. In addition, we also discuss a class enumerated by the binomial transform of the Catalan numbers and give conjectures for other equivalence classes of pattern-avoiding Fishburn permutations.
AB - The class of permutations that avoid the bivincular pattern (231 , { 1 } , { 1 }) is known to be enumerated by the Fishburn numbers. In this paper, we call them Fishburn permutations and study their pattern avoidance. For classical patterns of size 3, we give a complete enumerative picture for regular and indecomposable Fishburn permutations. For patterns of size 4, we focus on a Wilf equivalence class of Fishburn permutations that are enumerated by the Catalan numbers. In addition, we also discuss a class enumerated by the binomial transform of the Catalan numbers and give conjectures for other equivalence classes of pattern-avoiding Fishburn permutations.
UR - http://www.scopus.com/inward/record.url?scp=85075995132&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85075995132&partnerID=8YFLogxK
U2 - 10.1007/s00026-019-00463-6
DO - 10.1007/s00026-019-00463-6
M3 - Article
AN - SCOPUS:85075995132
SN - 0218-0006
VL - 23
SP - 785
EP - 800
JO - Annals of Combinatorics
JF - Annals of Combinatorics
IS - 3-4
ER -