Geodesic
Crossings and nestings for arc-coloured permutations and automation
Lily Yen1
1Capilano University and Simon Fraser University
The electronic journal of combinatorics, Tome 22 (2015) no. 1

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Zbl arXiv
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

Lily Yen  1

1 Capilano University and Simon Fraser University 
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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