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- Publications
- Influence

Basis-conjugating automorphisms of a free group and associated Lie algebras

- F. Cohen, J. Pakianathan, V. Vershinin, J. Wu
- Mathematics
- 30 October 2006

Let F_n = denote the free group with generators {x_1,...,x_n}. Nielsen and Magnus described generators for the kernel of the canonical epimorphism from the automorphism group of F_n to the general… Expand

Group actions and geometric combinatorics in 𝔽 q d $\mathbb{F}_{q}^{d}$

- M. Bennett, D. Hart, A. Iosevich, J. Pakianathan, M. Rudnev
- Mathematics
- 19 November 2013

Abstract In this paper we apply a group action approach to the study of Erdős–Falconer-type problems in vector spaces over finite fields and use it to obtain non-trivial exponents for the… Expand

Separation of Foreground Radiation from Cosmic Microwave Background Anisotropy Using Multifrequency Measurements

- W. Brandt, C. Lawrence, A. Readhead, J. Pakianathan, T. Fiola
- Physics
- 1 March 1994

The Fuglede conjecture holds in ℤp × ℤp

- A. Iosevich, A. Mayeli, J. Pakianathan
- Mathematics
- 9 May 2017

In the 70s Bent Fuglede conjectured that if Ω is bounded domain in R, then L(Ω) has an orthogonal basis of exponentials if and only if Ω tiles R by translation. This idea led to much activity and… Expand

Tiling sets and spectral sets over finite fields

We study tiling and spectral sets in vector spaces over prime fields. The classical Fuglede conjecture in locally compact abelian groups says that a set is spectral if and only if it tiles by… Expand

COHOMOLOGY OF UNIFORMLY POWERFUL p-GROUPS

- W. Browder, J. Pakianathan
- Mathematics
- 21 January 1999

In this paper we will study the cohomology of a family of p-groups associated to Fp-Lie algebras. More precisely we study a category BGrp of p-groups which will be equivalent to the category of… Expand

Long paths in the distance graph over large subsets of vector spaces over finite fields

- M. Bennett, J. Chapman, D. Covert, D. Hart, A. Iosevich, J. Pakianathan
- Mathematics, Medicine
- 31 May 2014

Let $E \subset {\Bbb F}_q^d$, the $d$-dimensional vector space over a finite field with $q$ elements. Construct a graph, called the distance graph of $E$, by letting the vertices be the elements of… Expand

Three-point configurations determined by subsets of $$\mathbb{F}_q^2$$ via the Elekes-Sharir Paradigm

- M. Bennett, A. Iosevich, J. Pakianathan
- Computer Science, Mathematics
- Comb.
- 24 January 2012

AbstractWe prove that if $$E \subset \mathbb{F}_Q^2$$, q ≡ 3 mod 4, has size greater than $$Cq^{\tfrac{7}
{4}}$$, then E determines a positive proportion of all congruence classes of triangles in… Expand

Geometric configurations in the ring of integers modulo $p^{\ell}$

- D. Covert, A. Iosevich, J. Pakianathan
- Mathematics
- 26 May 2011

We study variants of the Erd\H os distance problem and dot products problem in the setting of the integers modulo $q$, where $q = p^{\ell}$ is a power of an odd prime.

Threshold complexes and connections to number theory

- J. Pakianathan, Troy Winfree
- Mathematics
- 23 May 2013

In this paper we study quota complexes (or equivalently in the case of scalar weights, threshold complexes) and how the topology of these quota complexes changes as the quota is changed. This problem… Expand

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