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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Veröffentlicht in:Discrete mathematics and theoretical computer science Jg. DMTCS Proceedings, 28th...
Hauptverfasser: Mandelshtam, Olya, Viennot, Xavier
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Schlagworte:
[math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
ISSN:1365-8050, 1462-7264, 1365-8050
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Abstract 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.
AbstractList 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.
Author Mandelshtam, Olya
Viennot, Xavier
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  givenname: Xavier
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  organization: Laboratoire Bordelais de Recherche en Informatique
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Snippet In this paper, we introduce therhombic alternative tableaux, whose weight generating functions providecombinatorial formulae to compute the steady state...
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SubjectTerms [math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
Title Rhombic alternative tableaux, assemblees of permutations, and the ASEP
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