The poset of maximal tubings of the cycle graph is a lattice
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912640965541888 |
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| author | Adenbaum, Ben Barnard, Emily Hlavacek, Max Kagy, Bryson Lesnevich, Nathan R. T. Nasr, George D. Waddle, Katie |
| author_facet | Adenbaum, Ben Barnard, Emily Hlavacek, Max Kagy, Bryson Lesnevich, Nathan R. T. Nasr, George D. Waddle, Katie |
| contents | The poset of maximal tubings of a graph generalizes several well-known and remarkable partial orders. Notable examples include the weak Bruhat order and the Tamari lattice, posets of maximal tubings for the complete graph and the path graph, respectively. It is an open problem to characterize graphs for which the poset of maximal tubings is a lattice. In this paper, we prove that the poset of maximal tubings for the cycle graph is a lattice, and moreover that it is semidistributive and congruence uniform. As main tools, we characterize all order relations in the poset, and introduce a useful map from maximal tubings of the cycle graph to maximal tubings of the path graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The poset of maximal tubings of the cycle graph is a lattice Adenbaum, Ben Barnard, Emily Hlavacek, Max Kagy, Bryson Lesnevich, Nathan R. T. Nasr, George D. Waddle, Katie Combinatorics 06B10, 52B05, 06A07, 05E99 The poset of maximal tubings of a graph generalizes several well-known and remarkable partial orders. Notable examples include the weak Bruhat order and the Tamari lattice, posets of maximal tubings for the complete graph and the path graph, respectively. It is an open problem to characterize graphs for which the poset of maximal tubings is a lattice. In this paper, we prove that the poset of maximal tubings for the cycle graph is a lattice, and moreover that it is semidistributive and congruence uniform. As main tools, we characterize all order relations in the poset, and introduce a useful map from maximal tubings of the cycle graph to maximal tubings of the path graph. |
| title | The poset of maximal tubings of the cycle graph is a lattice |
| topic | Combinatorics 06B10, 52B05, 06A07, 05E99 |
| url | https://arxiv.org/abs/2510.09429 |