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math.CO2025
Notes on the topology of independence structures
Kevin Ivan Piterman, Volkmar Welker
Following Welsh, a pre-independence space (pi-space) is a set together with a non-empty collection of subsets of , called independent sets, which is closed under taki…
math.CO2025
Posets arising from decompositions of objects in a monoidal category
Kevin Ivan Piterman, Volkmar Welker
Given a symmetric monoidal category with product , where the neutral element for the product is an initial object, we consider the poset of -complemented subobj…
math.CO2024
The common basis complex and the partial decomposition poset
Benjamin Brück, Kevin I. Piterman, Volkmar Welker
For a finite-dimensional vector space , the common basis complex of is the simplicial complex whose vertices are the proper non-zero subspaces of , and is a simplex…