3 papers
math.CO2026
A combinatorial nerve theorem
Sucharita Barik, Anupam Mondal, Sajal Mukherjee +2
The celebrated (homological) nerve theorem makes use of spectral sequences to determine the homology of a space. However, this theorem cannot effectively compute the homology in ev…
math.CO2026
The number of Pfaffian orientations on punctured polygonally cellulated surfaces
Sajal Mukherjee, Pritam Chandra Pramanik, Arundhati Rakshit
In this paper, we introduce the notion of Pfaffian orientations on (punctured) polygonally cellulated orientable surfaces, and provide an expression for the number of such orientat…
math.CO2026
An effective Mayer-Vietoris Theorem for discrete Morse homology
Sajal Mukherjee, Pritam Chandra Pramanik, Arundhati Rakshit
The Mayer-Vietoris theorem is known for its wide applications, especially in determining homology. In fact, this theorem provides us with a long exact sequence, where the underlyin…