A Novel Insertion Algorithm

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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2024

Author dc:creator

• Quinlan, Isis

Chair dc:contributor.committeechair

• Shimozono, Mark M.

Committee members dc:contributor.committeemember

• Orr, Daniel D.
• Loehr, Nicholas A.
• Mihalcea, Constantin Leonardo

• algebraic combinatorics

Statement dc:rights

• Creative Commons Attribution 4.0 International

Licence dc:rights.uri

• http://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:40607

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/118942