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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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