7 papers
A Cubical Perspective on Complements of Union-Closed Families of Sets
Dhruv Bhasin
Complements of union-closed families of sets, over a finite ground set, are known as simply rooted families of sets. Cubical sets are widely studied topological objects having appl…
Generalized percolation games on the -dimensional square lattice, and ergodicity of associated probabilistic cellular automata
Dhruv Bhasin, Sayar Karmakar, Moumanti Podder +1
Each vertex of the infinite -dimensional square lattice graph is assigned, independently, a label that reads trap with probability , target with probability , and open wit…
Ergodicity of a generalized probabilistic cellular automaton with parity-based neighbourhoods
Dhruv Bhasin, Sayar Karmakar, Moumanti Podder +1
We study a one-dimensional generalized probabilistic cellular automaton with universe , alphabet , parameters and such that $0…
On a class of probabilistic cellular automata with size- neighbourhood and their applications in percolation games
Dhruv Bhasin, Sayar Karmakar, Moumanti Podder +1
Different versions of percolation games on , with parameters and that indicate, respectively, the probability with which a site in is label…
Combinatorial games on Galton-Watson trees involving several-generation-jump moves
Moumanti Podder, Dhruv Bhasin
We study the -jump normal and -jump misère games on rooted Galton-Watson trees, expressing the probabilities of various outcomes of these games as specific fixed points of ce…
Graph Polynomial for Colored Embedded Graphs: A Topological Approach
Somnath Basu, Dhruv Bhasin, Siddhartha Lal +1
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological wh…
Closures of Union-Closed Families
Dhruv Bhasin
Given a union-closed family of subsets of the universe , with not equal to the power set of , a new subset can be added to it such that th…