Deep Bhattacharjee

On the Hodge conjecture for Fermat varieties

LaTeX source (amsart, figures as PNG), compiled PDF and verification code for the paper On the Hodge conjecture for Fermat varieties by Deep Bhattacharjee. The paper proves the Hodge conjecture for the Fermat varieties of degrees 44 and 114 in every dimension, and more generally...

On the Hodge conjecture for Fermat varieties

LaTeX source (amsart, figures as PNG), compiled PDF and verification code for the paper On the Hodge conjecture for Fermat varieties by Deep Bhattacharjee. The paper proves the Hodge conjecture for the Fermat varieties of degrees 44, 51, 52 and 114 in every dimension, and more ge...

On the Hodge conjecture for Fermat varieties

LaTeX source (amsart, figures as PNG), compiled PDF and verification code for the paper On the Hodge conjecture for Fermat varieties by Deep Bhattacharjee. The paper proves the Hodge conjecture for the Fermat varieties of degrees 44, 52 and 114 in every dimension, and more genera...

On the Hodge conjecture for Fermat varieties

LaTeX source (amsart, figures as PNG), compiled PDF and verification code for the paper On the Hodge conjecture for Fermat varieties by Deep Bhattacharjee. The paper proves the Hodge conjecture for the Fermat varieties of degree 114 in every dimension, and more generally of every...

A counterexample to a conjecture of Graffiti.pc on the forest number

Conjecture 66 of Graffiti.pc, listed as open in Written on the Wall II, states that the order of a largest induced forest of a connected graph is at least twice the ceiling of the even mode of the degrees of its complement divided by its average degree. We show that it is false u...

Blowup above the exponent one third in viscous Katz-Pavlović dyadic models with small shell ratios

For the viscous Katz–Pavlović dyadic model with shell ratio Λ > 23/2, global regularity holds exactly for dissipation exponents α ≥ 1/3. We prove that this threshold is not universal: for Λ = 6/5, 13/10, 3/2, 17/10 and 9/5, suitable nonnegative finitely supported data lose regula...

Resolving Erdős–Ulam Monochromatic Union-Closed Family Conjectures

We prove both Erdős–Ulam conjectures on monochromatic union-closed families, which are the two specific questions of Erdős Problem 1183. Every two-colouring of the subsets of a finite set contains a monochromatic union-closed family whose size grows faster than any fixed power of...

On the ratio of surjective group homomorphisms to ring homomorphisms between cyclic rings

# Zenodo record: what to edit The archive already exists. It was created automatically from GitHub release v1.1.2. - Version DOI (cited in the paper): https://doi.org/10.5281/zenodo.23106785 - Concept DOI (always points to the newest version): https://doi.org/10.5281/zenodo.23106...

On the ratio of surjective group homomorphisms to ring homomorphisms between cyclic rings

# Zenodo record: what to edit The archive already exists. It was created automatically from GitHub release v1.1.2. - Version DOI (cited in the paper): https://doi.org/10.5281/zenodo.23106785 - Concept DOI (always points to the newest version): https://doi.org/10.5281/zenodo.23106...