We investigate permutations and involutions that avoid a pattern of length three and have a unique longest increasing subsequence (ULIS). We prove an explicit formula for 231-avoiders, we show that the growth rate for 321-avoiding permutations with a ULIS is 4, and prove that their generating function is not rational. We relate the case of 132-avoiders to the existing literature, raising some interesting questions. For involutions, we construct a bijection between 132-avoiding involutions with a ULIS and bidirectional ballot sequences.
@article{10_37236_9506,
author = {Mikl\'os B\'ona and Elijah DeJonge},
title = {Pattern avoiding permutations with a unique longest increasing subsequence},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {4},
doi = {10.37236/9506},
zbl = {1454.05006},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9506/}
}
TY - JOUR
AU - Miklós Bóna
AU - Elijah DeJonge
TI - Pattern avoiding permutations with a unique longest increasing subsequence
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/9506/
DO - 10.37236/9506
ID - 10_37236_9506
ER -
%0 Journal Article
%A Miklós Bóna
%A Elijah DeJonge
%T Pattern avoiding permutations with a unique longest increasing subsequence
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/9506/
%R 10.37236/9506
%F 10_37236_9506
Miklós Bóna; Elijah DeJonge. Pattern avoiding permutations with a unique longest increasing subsequence. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9506
