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arXiv · 1711.04747

An insertion algorithm over staircase tableaux compatible with the ASEP's matrix ansatz

Patxi Laborde-Zubieta
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Abstract

Based on the matrix ansatz of Derrida, Evans, Hakim and Pasquier, we prensent a new way of computing the stationary probability of a state of the asym- metric simple exclusion process (ASEP). Through an insertion algorithm over staircase tableaux, we give a combinatorial proof to the current interpretation of the ASEP by these tableaux of Corteel and Williams. The insertion algorithm induces a recursive structure which implies nice factorised formulas for the generating polynomials of staircase tableaux, as well as a bijection with some coloured inversion tables. In addi- tion, we adapt the insertion algorithm to the case of type B symmetric tableaux and we define a new matrix ansatz compatible with it.

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Patxi Laborde-Zubieta. 2017-11-13. An insertion algorithm over staircase tableaux compatible with the ASEP's matrix ansatz. https://arxiv.org/abs/1711.04747

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