6 papers
Lattice point sumsets and asymptotic approximate groups
Arindam Biswas, Pavlo Yatsyna
We establish new quantitative bounds for asymptotic approximate groups arising from finite subsets of lattices and, more generally, semi-linear subsets of abelian groups. Our appro…
On asymptotic approximate groups in nilpotent groups
Arindam Biswas
Let be a group and let be non-empty. We call an asymptotic -approximate group if, for a fixed dilation factor , the larger product sets ca…
Uniform two-generator presentations for with polynomial complexity bounds
Arindam Biswas
We give a uniform explicit construction of finite two-generator presentations for the special linear groups over the integers in all ranks at least three. The construction builds o…
On Chromatic Asymptotic Approximate Groups
Arindam Biswas
We study a chromatic theory of asymptotic approximate groups for tuples of subsets of abelian groups, combining Nathanson's chromatic sumset formalism with asymptotic covering idea…
Approximate Subloops in Moufang Loops
Arindam Biswas
We introduce a notion of finite approximate subloops in Moufang loops, with emphasis on the commutative case. For arbitrary Moufang loops we establish intrinsic product-set identit…
On the cop number and the weak Meyniel conjecture for algebraic graphs
Arindam Biswas, Jyoti Prakash Saha
We show that the cop number of the Cayley sum graph of a finite group with respect to a symmetric subset is at most twice its degree when the graph is connected, undirected…