Séminaire Lotharingien de Combinatoire, 78B.56 (2017), 12 pp.

Sylvie Corteel and Arthur Nunge

2-Species Exclusion Processes and Combinatorial Algebras

Abstract. 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.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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