Through the definition of a new insertion algorithm this paper seeks to provide an alternative to the existing bijections between permutations and certain kinds of tableaux. We will define two versions of each algorithm covered, both the existing ones and the novel one. These different constructions will include one using a lot of small intermediate steps and one which directly creates the tableaux from the permutation. After showing that these are equivalent, we will briefly discuss the results of pattern avoidance on tableau shape. / Doctor of Philosophy / Building up tableaux from permutations can be a helpful way to get information about that permutation without having to check by hand. Different methods of building tableaux will tell us different types of information about the permutation. For that reason, we are defining a new method of building tableaux so that we can extract useful information from the permutations used.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/118942 |
| Date | 09 May 2024 |
| Creators | Quinlan, Isis |
| Contributors | Mathematics, Shimozono, Mark M., Orr, Daniel D., Loehr, Nicholas A., Mihalcea, Constantin Leonardo |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | Creative Commons Attribution 4.0 International, http://creativecommons.org/licenses/by/4.0/ |
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