Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations
Defant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by establishing bijections between these cl...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2021-08-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6494/pdf |
| _version_ | 1827323736050630656 |
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| author | Hanna Mularczyk |
| author_facet | Hanna Mularczyk |
| author_sort | Hanna Mularczyk |
| collection | DOAJ |
| description | Defant, Engen, and Miller defined a permutation to be uniquely sorted if it
has exactly one preimage under West's stack-sorting map. We enumerate classes
of uniquely sorted permutations that avoid a pattern of length three and a
pattern of length four by establishing bijections between these classes and
various lattice paths. This allows us to prove nine conjectures of Defant. |
| first_indexed | 2024-03-11T21:31:40Z |
| format | Article |
| id | doaj.art-39f9205efe9545759afe1ca6d99bc6c6 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:57:14Z |
| publishDate | 2021-08-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-39f9205efe9545759afe1ca6d99bc6c62024-03-07T15:41:55ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502021-08-01vol. 22 no. 2, Permutation...Special issues10.46298/dmtcs.64946494Lattice Paths and Pattern-Avoiding Uniquely Sorted PermutationsHanna MularczykDefant, Engen, and Miller defined a permutation to be uniquely sorted if it has exactly one preimage under West's stack-sorting map. We enumerate classes of uniquely sorted permutations that avoid a pattern of length three and a pattern of length four by establishing bijections between these classes and various lattice paths. This allows us to prove nine conjectures of Defant.https://dmtcs.episciences.org/6494/pdfmathematics - combinatorics05a05, 05a15g.2.1 |
| spellingShingle | Hanna Mularczyk Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 05a05, 05a15 g.2.1 |
| title | Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations |
| title_full | Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations |
| title_fullStr | Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations |
| title_full_unstemmed | Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations |
| title_short | Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations |
| title_sort | lattice paths and pattern avoiding uniquely sorted permutations |
| topic | mathematics - combinatorics 05a05, 05a15 g.2.1 |
| url | https://dmtcs.episciences.org/6494/pdf |
| work_keys_str_mv | AT hannamularczyk latticepathsandpatternavoidinguniquelysortedpermutations |