Networks bijective to permutations
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866929237863170048 |
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| author | Shigechi, Keiichi |
| author_facet | Shigechi, Keiichi |
| contents | We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation through a Dyck tiling on a ribbon. We introduce a new combinatorial object similar to a tree-like tableau, which we call a forest. A forest is shown to give a permutation, and be bijective to a network corresponding to the inverse of the permutation. We show that the poset of networks is a finite graded lattice and admits an $EL$-labeling. By use of this $EL$-labeling, we show the lattice is supersolvable and compute the Möbius function of an interval of the poset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Networks bijective to permutations Shigechi, Keiichi Combinatorics We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation through a Dyck tiling on a ribbon. We introduce a new combinatorial object similar to a tree-like tableau, which we call a forest. A forest is shown to give a permutation, and be bijective to a network corresponding to the inverse of the permutation. We show that the poset of networks is a finite graded lattice and admits an $EL$-labeling. By use of this $EL$-labeling, we show the lattice is supersolvable and compute the Möbius function of an interval of the poset. |
| title | Networks bijective to permutations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.05600 |