Defines (P,φ)-Tamari lattices as a generalization of the Tamari lattice and uses them to establish join-semidistributivity and related properties for higher torsion class lattices of type A algebras.
Dimension of unicycle posets
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abstract
Motivated by the study of the dimension of random posets, it was conjectured by Bollob\'as and Brightwell in 1997 that if $P$ is a finite poset whose cover graph contains at most one cycle then its order dimension is at most $3$. In this paper we prove this conjecture by giving a constructive proof with explicit triplets of linear extensions realizing such posets.
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math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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$(P,\phi)$-Tamari and higher torsion lattices of type $\mathbf{A}$
Defines (P,φ)-Tamari lattices as a generalization of the Tamari lattice and uses them to establish join-semidistributivity and related properties for higher torsion class lattices of type A algebras.