Stanley's classification conjecture for indecomposable upho modular lattices
Stanley's classification conjecture for indecomposable upho modular lattices
Let be an upho modular lattice, meaning that is of finite type and its principal order filter at every element is isomorphic to . Suppose that is indecomposable and contains a complemented interval of rank . Stanley's classification conjecture. Then is isomorphic to the poset of submodules of of finite colength, ordered by reverse inclusion, for some local principal ideal domain with a finite residue field. This conjecture proposes that, apart from decomposable cases, these module posets account for upho modular lattices containing a complemented rank- interval; the paper records the conjecture but does not discuss its proof or status.
Sources & referencesView supporting material
Primary source
Yibo Gao, Joshua Guo, Karthik Seetharaman and Ilaria Seidel, “The Rank-Generating Functions of Upho Posets”, arXiv:2011.01916 (2020).
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