arXiv subjects
Publications and source records attributed to Chirantan Mukherjee.
We give an explicit description of the twisted arrow construction for simplicial spaces and demonstrate individually that it preserves the defining properties of a complete Segal space. Moreover, we show that for a Segal space, the natural projection from the twisted arrow Segal space is a left fibration.
The $\texttt{IntegerHull}$ function is part of Maple's $\texttt{PolyhedralSets}$ library, which calculates the integer hull of a given polyhedral set. This algorithm works by translating the supporting hyperplanes of the facets of the input polyhedral set inwards till each hyperplane encounters at least one integer point. The polyhedral set is then divided into smaller regions and a brute force method is applied to find the remaining vertices. There are certain edge case scenarios where the computational cost of the existing algorithm can be high, for which we propose a new algorithm. We translate the supporting hyperplanes of the facets inwards from the (relative) opposite vertex till the hyperplanes encounter at least one integer point. Then, we can follow the same procedure as the old algorithm or use a recursive technique on the smaller regions. The edge case scenarios mentioned above occurs when there are integer points present on the supporting hyperplanes of the facets of the polyhedral set. This increases the region on which the brute force method is applied to find the remaining vertices.