10 papers
Kneserized Anticoncentration and Reverse Absorption for Graham's Rearrangement Conjecture
Simone Costa, Stefano Della Fiore, Tao Feng +1
We establish a Kneser-based anticoncentration estimate for uniform subset sums in composite cyclic groups. The estimate contains a periodic loss and is weaker than its prime-modulu…
A note on vector trifferent codes over the Sphere
Stefano Della Fiore
Let be the unit sphere. A set is called vector trifferent if for every three distinct there is a coordinate for which $…
Slice and Partition Rank Criteria for Polynomial Zero-Avoidance
Simone Costa, Stefano Della Fiore, Mattia Fontana
We study polynomial zero-avoidance over finite vector spaces by means of slice rank and partition rank. We first make the support-entropy method effective by showing how a finite d…
Pareto-type finite-block optimality for source codes: a constrained Markov example
Stefano Della Fiore
We study a Pareto-type notion of finite-block optimality for injective source codes, where two codes are compared through the full sequence of expected block lengths. As a concrete…
Sharper upper bounds for -ary and constant-weight codes
Stefano Della Fiore
We derive refined entropy upper bounds for -ary codes by exploiting the Fourier structure of the i.i.d. difference distribution . Since the pmf of is an autocor…
Graham conjecture on small sets in abelian groups
Simone Costa, Stefano Della Fiore, Mattia Fontana +1
A famous conjecture of Graham asserts that every set can be ordered so that all partial sums are distinct. Although this conjecture was r…