2013/12/16 by Henri Mühle, Mühle, Henri
Computer Science · Mathematics · #06B05 (Primary) #06D15 #20F55 (Secondary) #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:06B05 #msc:06D15 #msc:20F55 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1312.4449
This paper has been withdrawn by the author due to a gap in the proof of Theorem 1.1(i). The results in Theorems 1.1(ii)-(iv) and 1.2, and those needed for their proofs remain true, and will be addressed in separate articles. I suspect that the claim of Theorem 1.1(i) is still true. In fact, I suspect that quotients of HH-lattices are HH-lattices again. Comments are very welcome
openalex publication_date 2013/12/16 · arxiv created 2015/01/09 · arxiv updated 2015/01/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The γ-Cambrian semilattices Cγ defined by Reading and Speyer are a family of meet-semilattices associated with a Coxeter group W and a Coxeter element γ∈ W, and they are lattices if and only if W is finite. In the case where W is the symmetric group \mathfrakSn and γ is the long cycle (1 2 … n) the corresponding γ-Cambrian lattice is isomorphic to the well-known Tamari lattice Tn. Recently, Kallipoliti and the author have investigated Cγ from a topological viewpoint, and showed that many properties of the Tamari lattices can be generalized nicely. In the present article this investigation is continued on a structural level using the observation of Reading and Speyer that Cγ is semidistributive. First we prove that every closed interval of Cγ is a bounded-homomorphic image of a free lattice (in fact it is a so-called H H-lattice). Subsequently we prove that each closed interval of Cγ is trim, we determine its breadth, and we characterize the closed intervals that are dismantlable.