Geodesic
Enumerations of permutations simultaneously avoiding a vincular and a covincular pattern of length 3
Journal of integer sequences, Tome 20 (2017) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Vincular and covincular patterns are generalizations of classical patterns allowing restrictions on the indices and values of the occurrences in a permutation. In this paper we study the integer sequences arising as the enumerations of permutations simultaneously avoiding a vincular and a covincular pattern, both of length 3, with at most one restriction. We see familiar sequences, such as the Catalan and Motzkin numbers, but also some previously unknown sequences which have close links to other combinatorial objects such as lattice paths and integer partitions. Where possible we include a generating function for the enumeration. One of the cases considered settles a conjecture by Pudwell (2010) on the Wilf-equivalence of barred patterns. We also give an alternative proof of the classic result that permutations avoiding 123 are counted by the Catalan numbers.
Keywords: permutation, pattern, covincular, enumeration, Wilf-equivalence 
@article{JIS_2017__20_7_a0,
     author = {Bean, Christian and Ulfarsson, Henning and Claesson, Anders},
     title = {Enumerations of permutations simultaneously avoiding a vincular and a covincular pattern of length 3},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {20},
     number = {7},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a0/}
}
TY  - JOUR
AU  - Bean, Christian
AU  - Ulfarsson, Henning
AU  - Claesson, Anders
TI  - Enumerations of permutations simultaneously avoiding a vincular and a covincular pattern of length 3
JO  - Journal of integer sequences
PY  - 2017
VL  - 20
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a0/
LA  - en
ID  - JIS_2017__20_7_a0
ER  - 
%0 Journal Article
%A Bean, Christian
%A Ulfarsson, Henning
%A Claesson, Anders
%T Enumerations of permutations simultaneously avoiding a vincular and a covincular pattern of length 3
%J Journal of integer sequences
%D 2017
%V 20
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a0/
%G en
%F JIS_2017__20_7_a0
Bean, Christian; Ulfarsson, Henning; Claesson, Anders. Enumerations of permutations simultaneously avoiding a vincular and a covincular pattern of length 3. Journal of integer sequences, Tome 20 (2017) no. 7. http://geodesic.mathdoc.fr/item/JIS_2017__20_7_a0/