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New dense superball packings in three dimensions

Publications associées (29)

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A simple proof for a forbidden subposet problem

Abhishek Methuku

The poset Y-k,Y-2 consists of k + 2 distinct elements x(1), x(2), ..., x(k), y(1), y(2), such that x(1)

ELECTRONIC JOURNAL OF COMBINATORICS2020

A Low-Parametric Rhombic Microstructure Family for Irregular Lattices

New fabrication technologies have significantly decreased the cost of fabrication of shapes with highly complex geometric structure. One important application of complex fine-scale geometric structures is to create variable effective elastic material prope ...

ASSOC COMPUTING MACHINERY2020

Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative semigroup actions

Florian Karl Richter

We establish two ergodic theorems which have among their corollaries numerous classical results from multiplicative number theory, including the Prime Number Theorem, a theorem of Pillai-Selberg, a theorem of Erd\H{o}s-Delange, the mean value theorem of Wi ...

2020

On the Number of Containments in P-free Families

Abhishek Methuku

A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p

Springer2019

Nested Convex Bodies are Chaseable

Marek Elias

In the Convex Body Chasing problem, we are given an initial point v0. Rd and an online sequence of n convex bodies F1,..., Fn. When we receive Ft, we are required to move inside Ft. Our goal is to minimize the total distance traveled. This fundamental onli ...

SPRINGER2019

Sharp sphere packings

Maryna Viazovska

In this talk we will speak about recent progress on the sphere packing problem. The packing problem can be formulated for a wide class of metric spaces equipped with a measure. An interesting feature of this optimization problem is that a slight change of ...

World Scientific Publishing2018

Almost tiling of the Boolean lattice with copies of a poset

Istvan Tomon

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...

ELECTRONIC JOURNAL OF COMBINATORICS2018

Building on Viazovska’s recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particul ...

2017

Possibility of an unconventional spin state of Ir4+ in Ba21Ir9O43 single crystal

László Forró, Henrik Moodysson Rønnow, Arnaud Magrez, Oleg Yazyev, Ivica Zivkovic, Alla Arakcheeva, Bálint Náfrádi, Lin Yang, Andrea Pisoni, Sergiy Katrych, Jacim Jacimovic, Noore Elahi Shaik

We report the synthesis of single crystals of a novel layered iridate Ba21Ir9O43 and present the crystallographic, transport, and magnetic properties of this material. The compound has a hexagonal structure with two iridium oxide layers stacked along the c ...

Amer Physical Soc2016

Cross-Intersecting Families of Vectors

János Pach, Gábor Tardos

Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinc ...

Springer Japan Kk2015