@article{Kouteck2021UniformAM,
title={Uniform and monotone line sum optimization},
author={Martin Kouteck{\'y} and Shmuel Onn},
journal={ArXiv},
year={2021},
volume={abs/2011.09932}
}

It is shown that deciding if a given sequence is the degree sequence of a 3-hypergraph is NP-complete, thereby solving a 30 year long open problem and implying that optimization over hypergraphs is hard already for simple concave functions.Expand

1. Introduction 2. Basic existence theorems for matrices with prescribed properties 3. The class A(R S) of (0,1)-matrices 4. More on the class A(R S) of (0,1)-matrices 5. The class T(R) of tournament… Expand

This paper is concerned with a matrix A of m rows and n columns, all of whose entries are 0's and l's. Let the sum of row i of A be denoted by r i (i = 1, … , m) and let the sum of column i of A be… Expand

A polynomial algorithm is provided that determines for any given undirected graph G=(V,E)$, positive integer $k$, and convex functions $f_v:\mathbb{N}\rightarrow\ mathbb{R}$ ($v\in V$) a subgraph of edges that minimizes f_v(d_H(v)$, where d_H (v) is the degree of v in $H$.Expand

Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of… Expand