9 papers
Resolving Erdős-Ulam Monochromatic Union-Closed Family Conjectures
Deep Bhattacharjee, Priyabrata Mandal, Ushashi Bhattacharya
We prove both Erdős-Ulam conjectures on monochromatic union-closed families. Every two-colouring of the subsets of a finite set contains a monochromatic union-closed family whose s…
The Sphere Packing Problem in Dimension 4 and the Twenty-Four-Cell Conjecture
Deep Bhattacharjee, Ushashi Bhattacharya, Priyabrata Mandal +1
We prove that every Voronoi cell of a unit-ball packing of has volume at least , with equality only at the configuration, so that the twenty-four-cell conje…
Spectral Algebras of Abelian Cayley Graphs
Deep Bhattacharjee, Priyabrata Mandal, Ushashi Bhattacharya
Let be a finite abelian group of order , a symmetric connection set, and a field with . The spectral algebra $\mathscr{A…
Norm Principles for and
Priyabrata Mandal
The aim of this article is to discuss the proof that the norm principle holds for the group of similitudes and the spinor group for a quadratic form $…
An Algebraic Approach to the Fundamental Theorem of Algebra
Priyabrata Mandal, Sajad A. Sheikh
In this paper, we investigate the algebraic counterpart of the Fundamental Theorem of Algebra. We explore the concept of real closed fields and quadratic forms. We show, by means o…
Totally positive field extensions and the pythagorean index
Priyabrata Mandal, Preeti Raman, Abhay Soman
For a formally real field , we study totally positive field extensions over . We show that, if is Galois and totally positive then so is the corresponding extensio…
Weak isotropy of central simple algebras with orthogonal involutions over totally positive field extensions
Priyabrata Mandal, Abhay Soman
In this paper, we explore the behavior of orthogonal involutions in the context of totally positive field extensions. Let be a totally positive extension of formally real fie…
Homomorphism Counts Quadratic Residues
Priyabrata Mandal, Sonu Kumar, Deep Bhattacharjee
We prove that the ratio of surjective group to ring homomorphism counts between finite cyclic rings admits three simultaneous interpretations that have n…
Characterization of Square Values and Power Sums of Consecutive Lucas Numbers
Priyabrata Mandal
We establish several Diophantine results involving Lucas and Fibonacci numbers. First, we prove that has the unique positive integer solution . We also show…