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math.CO2019
Partition and Cohen-Macaulay Extenders
Joseph Doolittle, Bennet Goeckner, Alexander Lazar
If a pure simplicial complex is partitionable, then its -vector has a combinatorial interpretation in terms of any partitioning of the complex. Given a non-partitionable complex…
math.CO2019
Minimal Cohen-Macaulay Simplicial Complexes
Hailong Dao, Joseph Doolittle, Justin Lyle
We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give suff…