Geodesic
Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding
Christian Bean1 ; Émile Nadeau2 ; Jay Pantone3 ; Henning Ulfarsson2
1Keele University
2Reykjavik University
3Marquette University
The electronic journal of combinatorics, Tome 31 (2024) no. 3
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We prove that any class of permutations defined by avoiding a partially ordered pattern (POP) with height at most two has a regular insertion encoding and thus has a rational generating function. Then, we use Combinatorial Exploration to find combinatorial specifications and generating functions for hundreds of other permutation classes defined by avoiding a size 5 POP, allowing us to resolve several conjectures of Gao and Kitaev (2019) and of Chen and Lin (2024).
DOI : 10.37236/12686
Classification : 05A05, 05A15, 68R15, 68W30
Mots-clés : permutation size, permutation classes

Christian Bean  1   ; Émile Nadeau  2   ; Jay Pantone  3   ; Henning Ulfarsson  2

1 Keele University
2 Reykjavik University
3 Marquette University 
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     title = {Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {3},
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}
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Christian Bean; Émile Nadeau; Jay Pantone; Henning Ulfarsson. Permutations avoiding bipartite partially ordered patterns have a regular insertion encoding. The electronic journal of combinatorics, Tome 31 (2024) no. 3. doi: 10.37236/12686

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