Improving bounds on packing densities of 4-point permutations
We consolidate what is currently known about packing densities of 4-point permutations and in the process improve the lower bounds for the packing densities of 1324 and 1342. We also provide rigorous upper bounds for the packing densities of 1324, 1342, and 2413. All our bounds are within $10^{-4}$...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2018-02-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3286/pdf |
| _version_ | 1797270063093383168 |
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| author | Jakub Sliacan Walter Stromquist |
| author_facet | Jakub Sliacan Walter Stromquist |
| author_sort | Jakub Sliacan |
| collection | DOAJ |
| description | We consolidate what is currently known about packing densities of 4-point
permutations and in the process improve the lower bounds for the packing
densities of 1324 and 1342. We also provide rigorous upper bounds for the
packing densities of 1324, 1342, and 2413. All our bounds are within $10^{-4}$
of the true packing densities. Together with the known bounds, this gives us a
fairly complete picture of all 4-point packing densities. We also provide new
upper bounds for several small permutations of length at least five. Our main
tool for the upper bounds is the framework of flag algebras introduced by
Razborov in 2007. |
| first_indexed | 2024-04-25T01:58:18Z |
| format | Article |
| id | doaj.art-33646e5e88d9455eab6c5df53bed70db |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:58:18Z |
| publishDate | 2018-02-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-33646e5e88d9455eab6c5df53bed70db2024-03-07T15:33:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502018-02-01Vol. 19 no. 2, Permutation...Permutation Patterns10.23638/DMTCS-19-2-33286Improving bounds on packing densities of 4-point permutationsJakub SliacanWalter StromquistWe consolidate what is currently known about packing densities of 4-point permutations and in the process improve the lower bounds for the packing densities of 1324 and 1342. We also provide rigorous upper bounds for the packing densities of 1324, 1342, and 2413. All our bounds are within $10^{-4}$ of the true packing densities. Together with the known bounds, this gives us a fairly complete picture of all 4-point packing densities. We also provide new upper bounds for several small permutations of length at least five. Our main tool for the upper bounds is the framework of flag algebras introduced by Razborov in 2007.https://dmtcs.episciences.org/3286/pdfmathematics - combinatorics |
| spellingShingle | Jakub Sliacan Walter Stromquist Improving bounds on packing densities of 4-point permutations Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics |
| title | Improving bounds on packing densities of 4-point permutations |
| title_full | Improving bounds on packing densities of 4-point permutations |
| title_fullStr | Improving bounds on packing densities of 4-point permutations |
| title_full_unstemmed | Improving bounds on packing densities of 4-point permutations |
| title_short | Improving bounds on packing densities of 4-point permutations |
| title_sort | improving bounds on packing densities of 4 point permutations |
| topic | mathematics - combinatorics |
| url | https://dmtcs.episciences.org/3286/pdf |
| work_keys_str_mv | AT jakubsliacan improvingboundsonpackingdensitiesof4pointpermutations AT walterstromquist improvingboundsonpackingdensitiesof4pointpermutations |