Journal article
A periodicity theorem for the octahedron recurrence
- Abstract:
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The octahedron recurrence lives on a 3-dimensional lattice and is given by f(x,y,t+1)=(f(x+1,y,t)f(x−1,y,t)+f(x,y+1,t)f(x,y−1,t))/f(x,y,t−1) . In this paper, we investigate a variant of this recurrence which lives in a lattice contained in [0,m]×[0,n]×R . Following Speyer, we give an explicit non-recursive formula for the values of this recurrence and use it to prove that it is periodic of period n+m. We then proceed to show various other hidden symmetries satisfied by this bounded octahedron recurrence.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 334.6KB, Terms of use)
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- Publisher copy:
- 10.1007/s10801-006-0045-0
Authors
- Publisher:
- Springer
- Journal:
- Journal of Algebraic Combinatorics More from this journal
- Volume:
- 26
- Issue:
- 1
- Pages:
- 1–26
- Publication date:
- 2007-01-09
- Acceptance date:
- 2006-10-26
- DOI:
- EISSN:
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1572-9192
- ISSN:
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0925-9899
- Keywords:
- Pubs id:
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pubs:693827
- UUID:
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uuid:9bbd3aa4-33a1-43be-a358-4805d30779ef
- Local pid:
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pubs:693827
- Source identifiers:
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693827
- Deposit date:
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2017-05-08
Terms of use
- Copyright holder:
- Springer Science+Business Media
- Copyright date:
- 2007
- Notes:
- © Springer Science+Business Media, LLC 2006. This is the accepted manuscript version of the article. The final version is available online from Springer at: https://doi.org/10.1007/s10801-006-0045-0
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