All Questions
4 questions
5
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289
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Cataland: Facets and partition polynomials of cluster complexes
Figure 25 on pg. 101 of "Cataland: Why the Fuss?" by Christian Stump, Hugh Thomas, and Nathan Williams depicts cluster complexes (CCs) associated with generalized $(m)$-Narayana / ...
- 10.5k
11
votes
1
answer
339
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Analogue of conic sections for the permutohedra, associahedra, and noncrossing partitions
Slicing cones in various ways with a plane generates conic sections identified geometrically as hyperbolas, parabolas, or ellipses and algebraically, when suitably rotated, as certain rescaled ...
- 10.5k
5
votes
1
answer
209
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If a finite poset supports a Cohen-Macaulay ASL, how far can it be from Cohen-Macaulay?
By the fundamental work of De Concini, Eisenbud, and Procesi, an algebra with straightening law (ASL) must be Cohen-Macaulay if it is built on a Cohen-Macaulay poset. I would like to understand the ...
- 2,851
12
votes
1
answer
285
views
Diameter of simplicial complex mirrored in property of Stanley-Reisner ring?
Consider a pure finite abstract simplicial complex $\Delta$. Define its diameter as the maximal distance between any two facets, i.e., between any two faces of maximal dimension $d-1$. The distance ...
- 907