Combinatorics of the 2-Species Exclusion Processes, Marked Laguerre Histories, and Partially Signed Permutations

Abstract

Starting from the two-species partially 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 a natural descent statistic on partially signed permutations; as well as partially signed permutations patterns.