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...
Uloženo v:
| Vydáno v: | Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th... |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
DMTCS
22.04.2020
Discrete Mathematics & Theoretical Computer Science |
| Témata: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Shrnutí: | 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. |
|---|---|
| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.46298/dmtcs.6320 |