Crossings and nestings for arc-coloured permutations and automation
The electronic journal of combinatorics, Tome 22 (2015) no. 1
Symmetric joint distribution between crossings and nestings was established in several combinatorial objects. Recently, Marberg extended Chen and Guo's result on coloured matchings to coloured set partitions following a multi-dimensional generalization of the bijection and enumerative methods from Chen, Deng, Du, Stanley, and Yan. We complete the study for arc-coloured permutations by establishing symmetric joint distribution for crossings and nestings and by showing that the ordinary generating functions for $j$-noncrossing, $k$-nonnesting, $r$-coloured permutations according to size $n$ are rational functions. Finally, we automate the generation of these rational functions and analyse the first $70$ series.
DOI :
10.37236/4080
Classification :
05A19, 05A18
Mots-clés : arc-coloured permutation, crossing, nesting, bijection, enumeration, tableau, generating tree, finite state automaton, transfer matrix, automation
Mots-clés : arc-coloured permutation, crossing, nesting, bijection, enumeration, tableau, generating tree, finite state automaton, transfer matrix, automation
Affiliations des auteurs :
Lily Yen 1
@article{10_37236_4080,
author = {Lily Yen},
title = {Crossings and nestings for arc-coloured permutations and automation},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4080},
zbl = {1305.05019},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4080/}
}
Lily Yen. Crossings and nestings for arc-coloured permutations and automation. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4080
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