Geodesic
2-Species Exclusion Processes and Combinatorial Algebras
Séminaire lotharingien de combinatoire, 78B (2017)

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Starting from the two-species asymmetric simple exclusion process, we study a subclass of signed permutations, the partially signed permutations, using the combinatorics of Laguerre histories. From this physical and bijective point of view, we obtain natural recoil and descent statistics on partially signed permutations. We define a new combinatorial algebra on these partially signed permutations and show that the segmented composition algebra defined by Novelli and Thibon is a subalgebra of this new algebra. This new point of view allows us to define a new basis for the segmented composition algebra with combinatorial properties. This generalizes classical combinatorial results on permutation and composition algebras. 

@article{SLC_2017_78B_a55,
     author = {Sylvie Corteel and Arthur Nunge},
     title = {2-Species {Exclusion} {Processes} and {Combinatorial} {Algebras}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a55/}
}
TY  - JOUR
AU  - Sylvie Corteel
AU  - Arthur Nunge
TI  - 2-Species Exclusion Processes and Combinatorial Algebras
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a55/
ID  - SLC_2017_78B_a55
ER  - 
%0 Journal Article
%A Sylvie Corteel
%A Arthur Nunge
%T 2-Species Exclusion Processes and Combinatorial Algebras
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a55/
%F SLC_2017_78B_a55
Sylvie Corteel; Arthur Nunge. 2-Species Exclusion Processes and Combinatorial Algebras. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a55/