5 papers
On a complete characterization of path-free complexes associated with complete multipartite graphs
Priyavrat Deshpande, Shuchita Goyal, Rutuja Sawant
Let be a graph and let $\PF_t(G)$ denote the simplicial complex whose faces are vertex subsets whose induced subgraphs contain no path on vertices. These complexes encode a…
Vertex decomposable complexes of directed forests, conflict graphs and chordality
Priyavrat Deshpande, Rutuja Sawant
Let be a multidigraph. We study the simplicial complex , whose vertices are the directed edges of and whose faces correspond to directed linear forests, th…
The complex of -co-connected subgraphs, chordality and Fröberg's theorem
Priyavrat Deshpande, Amit Roy, Rutuja Sawant
We introduce a new family of pure simplicial complexes, called the -co-connected complex of with respect to , , where is a natural number, is a s…
Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning
Priyavrat Deshpande, Aditya Karnataki, Pratiksha Shingavekar
This article presents a comprehensive data-scientific investigation into the arithmetic statistics of congruent number elliptic curves, leveraging a dataset of square-free integers…
Real Bott manifold structure of -dimensional Klein bottle and its rational Betti numbers
Navnath Daundkar, Priyavrat Deshpande
Donald Davis initiated the study of an -dimensional analogue of the Klein bottle. This generalized Klein bottle occurs as a moduli space of planar polygons for a certain choice…