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Dynamics of plane partitions Pechenik, Oliver
Description
Consider a plane partition $P$ as an order ideal in the product $[a] \times [b] \times [c]$ of three chain posets. The combinatorial rowmotion operator sends $P$ to the plane partition generated by the minimal elements of its complement. What is the orbit structure of this action I will attempt to survey the state of this question. In particular, I will describe my recent work with Becky Patrias, showing that rowmotion exhibits a strong form of resonance with frequency $a+b+c-1$, in the sense that each orbit size shares a prime divisor with $a+b+c-1$. This confirms a 1995 conjecture of Peter Cameron and Dmitri Fon-Der-Flaass.
Item Metadata
Title |
Dynamics of plane partitions
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-10-21T09:00
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Description |
Consider a plane partition $P$ as an order ideal in the product $[a] \times [b] \times [c]$ of three chain posets. The combinatorial rowmotion operator sends $P$ to the plane partition generated by the minimal elements of its complement. What is the orbit structure of this action I will attempt to survey the state of this question. In particular, I will describe my recent work with Becky Patrias, showing that rowmotion exhibits a strong form of resonance with frequency $a+b+c-1$, in the sense that each orbit size shares a prime divisor with $a+b+c-1$. This confirms a 1995 conjecture of Peter Cameron and Dmitri Fon-Der-Flaass.
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Extent |
43.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Michigan
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Series | |
Date Available |
2021-04-20
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0396766
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International