Deep Bhattacharjee

collaborators

4 papers

math.CO2026

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…

math.NT2026

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 $R^{4}$ has volume at least $8$ , with equality only at the $D_{4}$ configuration, so that the twenty-four-cell conje…

math.NT2026

Spectral Algebras of Abelian Cayley Graphs

Deep Bhattacharjee, Priyabrata Mandal, Ushashi Bhattacharya

Let $G$ be a finite abelian group of order $N$ , $S \subseteq G ∖ {0}$ a symmetric connection set, and $K$ a field with $c ha r (K) ∤ N$ . The spectral algebra $\mathscr{A…

math.AC2025

Homomorphism Counts Quadratic Residues

Priyabrata Mandal, Sonu Kumar, Deep Bhattacharjee

We prove that the ratio $ϱ (n) = ϕ (n) / 2^{ω (n)}$ of surjective group to ring homomorphism counts between finite cyclic rings admits three simultaneous interpretations that have n…