Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2016
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| Online Access: | http://hdl.handle.net/1721.1/104603 |
| _version_ | 1811081263841280000 |
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| author | Engel Shaposhnik, Efrat |
| author2 | Richard P. Stanley. |
| author_facet | Richard P. Stanley. Engel Shaposhnik, Efrat |
| author_sort | Engel Shaposhnik, Efrat |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. |
| first_indexed | 2024-09-23T11:43:59Z |
| format | Thesis |
| id | mit-1721.1/104603 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T11:43:59Z |
| publishDate | 2016 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1046032019-04-12T16:27:31Z Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains Engel Shaposhnik, Efrat Richard P. Stanley. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics. Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016. Cataloged from PDF version of thesis. Includes bibliographical references (page 87). This thesis consists of two parts. In the first part we count antichains of interval orders and in particular semiorders. We associate a Dyck path to each interval order, and give a formula for the number of antichains of an interval order in terms of the corresponding Dyck path. We then use this formula to give a generating function for the total number of antichains of semiorders, enumerated by the sizes of the semiorders and the antichains. In the second part we expand the work of Liu and Stanley on Dilworth lattices. Let L be a distributive lattice, let -(L) be the maximum number of elements covered by a single element in L, and let K(L) be the subposet of L consisting of the elements that cover o-(L) elements. By a result of Dilworth, K(L) is also a distributive lattice. We compute o(L) and K(L) for various lattices L that arise as the coordinate-wise partial ordering on certain sets of semistandard Young tableaux. by Efrat Engel Shaposhnik. Ph. D. 2016-09-30T19:37:53Z 2016-09-30T19:37:53Z 2016 2016 Thesis http://hdl.handle.net/1721.1/104603 958839493 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 87 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Engel Shaposhnik, Efrat Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains |
| title | Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains |
| title_full | Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains |
| title_fullStr | Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains |
| title_full_unstemmed | Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains |
| title_short | Antichains of interval orders and semiorders, and Dilworth lattices of maximum size antichains |
| title_sort | antichains of interval orders and semiorders and dilworth lattices of maximum size antichains |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/104603 |
| work_keys_str_mv | AT engelshaposhnikefrat antichainsofintervalordersandsemiordersanddilworthlatticesofmaximumsizeantichains |