We show that, given a suitable combinatorial specification for a permutation class $\mathcal{C}$, one can obtain a specification for the juxtaposition (on either side) of $\mathcal{C}$ with Av(21) or Av(12), and that if the enumeration for $\mathcal{C}$ is given by a rational or algebraic generating function, so is the enumeration for the juxtaposition. Furthermore this process can be iterated, thereby providing an effective method to enumerate any `skinny' $k\times 1$ grid class in which at most one cell is non-monotone, with a guarantee on the nature of the enumeration given the nature of the enumeration of the non-monotone cell.
@article{10_37236_8700,
author = {Robert Brignall and Jakub Slia\v{c}an},
title = {Combinatorial specifications for juxtapositions of permutation classes},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8700},
zbl = {1422.05002},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8700/}
}
TY - JOUR
AU - Robert Brignall
AU - Jakub Sliačan
TI - Combinatorial specifications for juxtapositions of permutation classes
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8700/
DO - 10.37236/8700
ID - 10_37236_8700
ER -
%0 Journal Article
%A Robert Brignall
%A Jakub Sliačan
%T Combinatorial specifications for juxtapositions of permutation classes
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8700/
%R 10.37236/8700
%F 10_37236_8700
Robert Brignall; Jakub Sliačan. Combinatorial specifications for juxtapositions of permutation classes. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8700
