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arxiv: 2505.16837 · v2 · pith:4ALQCQ4Nnew · submitted 2025-05-22 · 🧮 math.CO

Dimension of unicycle posets

Antoine Abram , Adrien Segovia This is my paper
classification 🧮 math.CO
keywords dimensionposetsbollobbrightwellconjectureconjecturedconstructivecontains
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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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  1. $(P,\phi)$-Tamari and higher torsion lattices of type $\mathbf{A}$

    math.CO 2026-05 unverdicted novelty 7.0

    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.