20 citations · 78 across the 40 of their papers we have counts for
53 papers
Pairs of lattice complements with complementary homology
Sara Faridi, Dharm Veer, Volkmar Welker
In this paper we study whether there is a global to local principle for the homology of order complexes of finite lattices. We explore whether the non-vanishing of the homology of…
Simplicial Complexes of Antichains in Root Posets and Related Combinatorics of Dyck Paths
Lili Mu, Volkmar Welker
For a crystallographic root system we consider the simplicial complex of all antichains in the root poset of . We show that $Δ_{\ma…
Generalized binomial edge ideals are Cartwright-Sturmfels
Aldo Conca, Emanuela De Negri, Volkmar Welker
Binomial edge ideals associated to a simple graph G were introduced by Herzog and collaborators and, independently, by Ohtani. They became an ``instant classic" in combinatorial co…
Posets of decompositions in spherical buildings
Kevin Ivan Piterman, John Shareshian, Volkmar Welker
We propose definitions of the common bases complex, the poset of decompositions, and the poset of partial decompositions for arbitrary spherical buildings. We show that the poset o…
On the homology of simplicial and cubical sets with symmetries
Curtis Greene, Volkmar Welker, Georg Wille
We study the homology of simplicial and cubical sets with symmetries. These are simplicial and cubical sets with additional maps expressing the symmetries of simplices and cubes. W…
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…