7 papers
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…
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…
Cancellation of a critical pair in discrete Morse theory and its effect on (co)boundary operators
Anupam Mondal, Sajal Mukherjee, Pritam Chandra Pramanik
Discrete Morse theory helps us compute the homology groups of simplicial complexes in an efficient manner. A "good" gradient vector field reduces the number of critical simplices,…
-colourability of the maximum ranked elements of a combinatorially sphere-like ranked poset
Anupam Mondal, Sajal Mukherjee, Pritam Chandra Pramanik
We obtain a higher dimensional analogue of a classical theorem which states that a polygonally cellulated -sphere in , such that each vertex has even degree, is $2…
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…
Combinatorial degree version of a generalized -Tucker's lemma with a combinatorial proof
Sajal Mukherjee, Pritam Chandra Pramanik
Combinatorial analogues of classical Borsuk-Ulam-type theorems (e.g., Tucker's lemma, -Tucker's lemma, etc.) have numerous important applications in combinatorics. In…