Characterizing Rothe Diagrams
| Autor: | Gillen, Ben, Michala, Jonathan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Rothe diagrams are diagrams which track inversions of a permutation. We define six main properties that Rothe diagrams fulfill: the southwest, dot, popping, numbering, step-out avoiding, and empty cell gap rules. We prove that -- given an arbitrary bubble diagram -- four different subsets of these properties provide sufficient criteria for the diagram to be a Rothe diagram. We also prove that when a set of ordered, freely floating, non-empty columns satisfy the numbering and step-out avoiding rules, then they can be arranged into a Rothe diagram. Comment: 14 pages, 9 figures |
| Databáze: | arXiv |
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