Arindam Biswas

activity

20152026

most citedOn minimal complements in groups

14 citations · 42 across the 19 of their papers we have counts for

collaborators

22 papers

math.CO2026

Fast robbers on abelian Cayley graphs and digraphs

Arindam Biswas

We study the fast-robber version of the Cops and Robbers game on finite strongly connected abelian Cayley digraphs, including undirected Cayley graphs as the symmetric case. For bo…

math.NT2026

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…

math.GR2026

On asymptotic approximate groups in nilpotent groups

Arindam Biswas

Let $G$ be a group and let $A \subseteq G$ be non-empty. We call $A$ an asymptotic $(r, l)$ -approximate group if, for a fixed dilation factor $r$ , the larger product sets $A^{h r}$ ca…

math.GR2026

Uniform two-generator presentations for $S L_{n} (Z)$ 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…

math.CO2026

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…

math.CO2023

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 $G$ with respect to a symmetric subset $S$ is at most twice its degree when the graph is connected, undirected…

math.CO2020

Spectrum of twists of Cayley and Cayley sum graphs

Arindam Biswas, Jyoti Prakash Saha

Let $G$ be a finite group with $∣ G ∣ \geq 4$ and $S$ be a subset of $G$ . Given an automorphism $σ$ of $G$ , the twisted Cayley graph $C (G, S)^{σ}$ (resp. the twisted Cayley sum graph $C…

math.CO2020★ 1 cited

Asymptotic behaviour of minimal complements

Arindam Biswas, Jyoti Prakash Saha

The notion of minimal complements was introduced by Nathanson in 2011 as a natural group-theoretic analogue of the metric concept of nets. Given two non-empty subsets $W, W^{'}$ in a g…

math.CO2020★ 4 cited

On non-minimal complements

Arindam Biswas, Jyoti Prakash Saha

The notion of minimal complements was introduced by Nathanson in 2011. Since then, the existence or the inexistence of minimal complements of sets have been extensively studied. Re…

math.NT2020★ 1 cited

Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions

Arindam Biswas, Jyoti Prakash Saha

The study of minimal complements in a group or a semigroup was initiated by Nathanson. The notion of minimal complements and being a minimal complement leads to the notion of co-mi…

math.NT2020★ 1 cited

Infinite co-minimal pairs in the integers and integral lattices

Arindam Biswas, Jyoti Prakash Saha

Given two nonempty subsets $A, B$ of a group $G$ , they are said to form a co-minimal pair if $A \cdot B = G$ , and $A^{'} \cdot B ⊊ G$ for any $\emptyset \neq = A^{'} ⊊ A$ …

math.CO2019

Flexibility and movability in Cayley graphs

Arindam Biswas

Let $Γ = (V, E)$ be a (non-trivial) finite graph with $λ : E \to R_{+}$ , an edge labelling of $Γ$ . Let $ρ : V \to R^{2}$ be a map which…

math.CO2019

A Cheeger type inequality in finite Cayley sum graphs

Arindam Biswas, Jyoti Prakash Saha

Let $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $∣ S ∣ = d$ . We show that if the undirected Cayley sum graph $C_{Σ} (G, S)$ is an expander graph and is non-bi…

math.CO2019★ 7 cited

On additive co-minimal pairs

Arindam Biswas, Jyoti Prakash Saha

A pair of non-empty subsets $(W, W^{'})$ in an abelian group $G$ is an additive complement pair if $W + W^{'} = G$ . $W^{'}$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \foral…

math.NT2019★ 1 cited

On semilinear sets and asymptotically approximate groups

Arindam Biswas, Wolfgang Alexander Moens

Let $G$ be any group and $A$ be an arbitrary subset of $G$ (not necessarily symmetric and not necessarily containing the identity). The $h$ -fold product set of $A$ is defined as $$…

math.CO2019★ 1 cited

Minimal additive complements in finitely generated abelian groups

Arindam Biswas, Jyoti Prakash Saha

Given two non-empty subsets $W, W^{'} \subseteq G$ in an arbitrary abelian group $G$ , $W^{'}$ is said to be an additive complement to $W$ if $W + W^{'} = G$ and it is minimal if no proper subse…

math.NT2019★ 3 cited

Asymptotic complements in the integers

Arindam Biswas, Jyoti Prakash Saha

Let $W \subseteq Z$ be a non-empty subset of the integers. A nonempty set $C \subseteq Z$ is said to be an asymptotic complement to $W$ if $W + C$ contains almost all…

math.CO2018★ 14 cited

On minimal complements in groups

Arindam Biswas, Jyoti Prakash Saha

Let $W, W^{'} \subseteq G$ be nonempty subsets in an arbitrary group $G$ . The set $W^{'}$ is said to be a complement to $W$ if $W W^{'} = G$ and it is minimal if no proper subset of $W^{'}$ is a co…

math.GR2018★ 5 cited

Logarithmic girth expander graphs of $S L_{n} (F_{p})$

Goulnara Arzhantseva, Arindam Biswas

We provide an explicit construction of finite 4-regular graphs $(Γ_{k})_{k \in N}$ with $g i r t h Γ_{k} \to \infty$ as $k \to \infty$ and $\frac{d iam Γ _{k}}{g i r t h Γ _{k}} ⩽ D$ for…

math.GR2018

On a cheeger type inequality in Cayley graphs of finite groups

Arindam Biswas

Let $G$ be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph $C (G, S)$ is an expander graph and is non-bipartite then the spectrum of the ad…

math.GR2018

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…

math.GR2015★ 4 cited

Diameter Bound for Finite Simple Groups of Large Rank

Arindam Biswas, Yilong Yang

Given a non-abelian finite simple group $G$ of Lie type, and an arbitrary generating set $S$ , it is conjectured by Laszlo Babai that its Cayley graph $Γ (G, S)$ will have a diameter…

Fast robbers on abelian Cayley graphs and digraphs

Lattice point sumsets and asymptotic approximate groups

On asymptotic approximate groups in nilpotent groups

Uniform two-generator presentations for SLn​(Z) with polynomial complexity bounds

On Chromatic Asymptotic Approximate Groups

On the cop number and the weak Meyniel conjecture for algebraic graphs

Spectrum of twists of Cayley and Cayley sum graphs

Asymptotic behaviour of minimal complements

On non-minimal complements

Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions

Infinite co-minimal pairs in the integers and integral lattices

Flexibility and movability in Cayley graphs

A Cheeger type inequality in finite Cayley sum graphs

On additive co-minimal pairs

On semilinear sets and asymptotically approximate groups

Minimal additive complements in finitely generated abelian groups

Asymptotic complements in the integers

On minimal complements in groups

Logarithmic girth expander graphs of SLn​(Fp​)

On a cheeger type inequality in Cayley graphs of finite groups

Approximate Subloops in Moufang Loops

Diameter Bound for Finite Simple Groups of Large Rank

Uniform two-generator presentations for $S L_{n} (Z)$ with polynomial complexity bounds

Logarithmic girth expander graphs of $S L_{n} (F_{p})$