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dc.contributor.authorRhee, Donguk 15:00:46 (GMT) 15:00:46 (GMT)
dc.description.abstractCyclic sieving phenomenon (CSP) is a generalization by Reiner, Stanton, White of Stembridge's q=-1 phenomenon. When CSP is exhibited, orbits of a cyclic action on combinatorial objects show a nice structure and their sizes can be encoded by one polynomial. In this thesis we study various proofs of a very interesting cyclic sieving phenomenon, that jeu-de-taquin promotion on rectangular Young tableaux exhibits CSP. The first proof was obtained by Rhoades, who used Kazhdan-Lusztig representation. Purbhoo's proof uses Wronski map to equate tableaux with points in the fibre of the map. Finally, we consider Petersen, Pylyavskyy, Rhoades's proof on 2 and 3 row tableaux by bijecting the promotion of tableaux to rotation of webs. This thesis also propose a combinatorial approach to prove the CSP for square tableaux. A variation of jeu-de-taquin move yields a way to count square tableaux which has minimal orbit under promotion. These tableaux are then in bijection to permutations. We consider how this can be generalized.en
dc.publisherUniversity of Waterlooen
dc.subjectCyclic sieving phenomenonen
dc.titleCyclic Sieving Phenomenon of Promotion on Rectangular Tableauxen
dc.typeMaster Thesisen
dc.subject.programCombinatorics and Optimizationen and Optimizationen
uws-etd.degreeMaster of Mathematicsen

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