Rhombic alternative tableaux, assemblees of permutations, and the ASEP
In this paper, we introduce therhombic alternative tableaux, whose weight generating functions providecombinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there aretwo species of particles, oneheavyand onelight, on a one-dimensional finite lattice wi...
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| Published in: | Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 28th... |
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| Main Authors: | , |
| Format: | Journal Article Conference Proceeding |
| Language: | English |
| Published: |
DMTCS
22.04.2020
Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| Online Access: | Get full text |
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| Summary: | In this paper, we introduce therhombic alternative tableaux, whose weight generating functions providecombinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there aretwo species of particles, oneheavyand onelight, on a one-dimensional finite lattice with open boundaries, and theparametersα,β, andqdescribe the hopping probabilities. The rhombic alternative tableaux are enumerated by theLah numbers, which also enumerate certainassembl ́ees of permutations. We describe a bijection between the rhombicalternative tableaux and these assembl ́ees. We also provide an insertion algorithm that gives a weight generatingfunction for the assemb ́ees. Combined, these results give a bijective proof for the weight generating function for therhombic alternative tableaux. |
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| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.6320 |