Geodesic
Semi-Baxter and Strong-Baxter Permutations
Séminaire lotharingien de combinatoire, 78B (2017)

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In this paper, we enumerate two families of pattern-avoiding permutations: those avoiding the vincular pattern 2\underbracket{41}3, which we call semi-Baxter permutations, and those avoiding the vincular patterns 2\underbracket{41}3, 3\underbracket{14}2 and 3\underbracket{41}2, which we call strong-Baxter permutations. For each of these families, we describe a generating tree, which translates into a functional equation for the generating function. For semi-Baxter permutations, it is solved using (a variant of) the kernel method, giving an expression for the generating function and both a closed and a recursive formula for its coefficients. For strong-Baxter permutations, we show that their generating function is (a slight modification of) that of a family of walks in the quarter plane, which is known to be non D-finite. 

@article{SLC_2017_78B_a18,
     author = {Mathilde Bouvel and Veronica Guerrini and Andrew Rechnitzer and Simone Rinaldi},
     title = {Semi-Baxter and {Strong-Baxter} {Permutations}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a18/}
}
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AU  - Mathilde Bouvel
AU  - Veronica Guerrini
AU  - Andrew Rechnitzer
AU  - Simone Rinaldi
TI  - Semi-Baxter and Strong-Baxter Permutations
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a18/
ID  - SLC_2017_78B_a18
ER  - 
%0 Journal Article
%A Mathilde Bouvel
%A Veronica Guerrini
%A Andrew Rechnitzer
%A Simone Rinaldi
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%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a18/
%F SLC_2017_78B_a18
Mathilde Bouvel; Veronica Guerrini; Andrew Rechnitzer; Simone Rinaldi. Semi-Baxter and Strong-Baxter Permutations. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a18/