7 papers · 1 filter
A combinatorial nerve theorem for effective homology computation
Sucharita Barik, Anupam Mondal, Sajal Mukherjee +2
The celebrated (homological) nerve theorem makes use of spectral sequences to determine the homology of a simplicial complex. However, this theorem cannot effectively compute the h…
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…
-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…
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,…
A note on an application of discrete Morse theoretic techniques on the complex of disconnected graphs
Anupam Mondal, Pritam Chandra Pramanik
Robin Forman's highly influential 2002 paper A User's Guide to Discrete Morse Theory presents an overview of the subject in a very readable manner. As a proof of concept, the autho…