Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture
One of the oldest outstanding problems in dynamical algebraic combinatorics is the following conjecture of P. Cameron and D. Fon-Der-Flaass (1995): consider a plane partition P in an $a \times b \times c$ box ${\sf B}$ . Let $\Psi (P)$ denote the smallest plane partition conta...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2020-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509420000614/type/journal_article |
| _version_ | 1811156204144033792 |
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| author | Rebecca Patrias Oliver Pechenik |
| author_facet | Rebecca Patrias Oliver Pechenik |
| author_sort | Rebecca Patrias |
| collection | DOAJ |
| description | One of the oldest outstanding problems in dynamical algebraic combinatorics is the following conjecture of P. Cameron and D. Fon-Der-Flaass (1995): consider a plane partition P in an
$a \times b \times c$
box
${\sf B}$
. Let
$\Psi (P)$
denote the smallest plane partition containing the minimal elements of
${\sf B} - P$
. Then if
$p= a+b+c-1$
is prime, Cameron and Fon-Der-Flaass conjectured that the cardinality of the
$\Psi $
-orbit of P is always a multiple of p. |
| first_indexed | 2024-04-10T04:47:35Z |
| format | Article |
| id | doaj.art-d201b82c1d7f4c4eae7b85bbac606a10 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:35Z |
| publishDate | 2020-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-d201b82c1d7f4c4eae7b85bbac606a102023-03-09T12:34:47ZengCambridge University PressForum of Mathematics, Sigma2050-50942020-01-01810.1017/fms.2020.61Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjectureRebecca Patrias0Oliver Pechenik1https://orcid.org/0000-0002-7090-2072Department of Mathematics, University of St. Thomas, St. Paul, MN 55105, USA; E-mail:Department of Combinatorics & Optimization, University of Waterloo, Waterloo, ON N2L 3G1, Canada; E-mail:One of the oldest outstanding problems in dynamical algebraic combinatorics is the following conjecture of P. Cameron and D. Fon-Der-Flaass (1995): consider a plane partition P in an $a \times b \times c$ box ${\sf B}$ . Let $\Psi (P)$ denote the smallest plane partition containing the minimal elements of ${\sf B} - P$ . Then if $p= a+b+c-1$ is prime, Cameron and Fon-Der-Flaass conjectured that the cardinality of the $\Psi $ -orbit of P is always a multiple of p.https://www.cambridge.org/core/product/identifier/S2050509420000614/type/journal_article05E1805A17 |
| spellingShingle | Rebecca Patrias Oliver Pechenik Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture Forum of Mathematics, Sigma 05E18 05A17 |
| title | Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture |
| title_full | Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture |
| title_fullStr | Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture |
| title_full_unstemmed | Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture |
| title_short | Dynamics of plane partitions: Proof of the Cameron–Fon-Der-Flaass conjecture |
| title_sort | dynamics of plane partitions proof of the cameron fon der flaass conjecture |
| topic | 05E18 05A17 |
| url | https://www.cambridge.org/core/product/identifier/S2050509420000614/type/journal_article |
| work_keys_str_mv | AT rebeccapatrias dynamicsofplanepartitionsproofofthecameronfonderflaassconjecture AT oliverpechenik dynamicsofplanepartitionsproofofthecameronfonderflaassconjecture |