5 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…
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 recursive construction of an acyclic matching on the independence complex of a graph with a simplicial vertex
Sucharita Barik, Anupam Mondal, Sajal Mukherjee
We provide a recursive construction of an acyclic matching (also known as a gradient vector field, an equivalent notion to a discrete Morse function) on the independence complex of…
-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…
Corrigendum to "Topology of matching complexes of complete graphs via discrete Morse theory'' [arXiv:2305.02973, Discrete Math. Theor. Comput. Sci. 26:3#13 (2024)]
Anupam Mondal, Sajal Mukherjee, Kuldeep Saha
In this corrigendum to arXiv:2305.02973, we justify that the motivation behind Conjecture 5.1 is based on a mistaken notion. Moreover, we prove a stronger theorem that disproves th…