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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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/6320/pdf |
| _version_ | 1797270233164021760 |
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| author | Olya Mandelshtam Xavier Viennot |
| author_facet | Olya Mandelshtam Xavier Viennot |
| author_sort | Olya Mandelshtam |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:01:00Z |
| format | Article |
| id | doaj.art-c065b8cea28148a9915238c2ef087814 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:00Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-c065b8cea28148a9915238c2ef0878142024-03-07T14:55:21ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63206320Rhombic alternative tableaux, assemblees of permutations, and the ASEPOlya Mandelshtam0Xavier Viennot1Department of Mathematics [Berkeley]Laboratoire Bordelais de Recherche en InformatiqueIn 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.https://dmtcs.episciences.org/6320/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Olya Mandelshtam Xavier Viennot Rhombic alternative tableaux, assemblees of permutations, and the ASEP Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Rhombic alternative tableaux, assemblees of permutations, and the ASEP |
| title_full | Rhombic alternative tableaux, assemblees of permutations, and the ASEP |
| title_fullStr | Rhombic alternative tableaux, assemblees of permutations, and the ASEP |
| title_full_unstemmed | Rhombic alternative tableaux, assemblees of permutations, and the ASEP |
| title_short | Rhombic alternative tableaux, assemblees of permutations, and the ASEP |
| title_sort | rhombic alternative tableaux assemblees of permutations and the asep |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6320/pdf |
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