Minimum supports of eigenfunctions of graphs: a survey Page 1 Minimum supports of
eigenfunctions of graphs: a survey ⋆ Ev Sotnikovaa, Alexandr Valyuzhenicha,∗ aSobolev Institute …

Suppose that we have a set S of n real numbers which have nonnegative sum. How few
subsets of S of order k can have nonnegative sum? Manickam, Miklós, and Singhi …

An r-unform n-vertex hypergraph H is said to have the Manickam-Mikl\'os-Singhi (MMS)
property if for every assignment of weights to its vertices with nonnegative sum, the number …

Three $ k $-dimensional subspaces $ A $, $ B $, and $ C $ of an $ n $-dimensional vector
space $ V $ over a finite field are called a $3 $-cluster if $ A\cap B\cap C=\{\mathbf {0} _V\} …

Let V be an n-dimensional vector space over a finite field with q elements. Define a real-
valued weight function on the 1-dimensional subspaces of V such that the sum of all weights …

We show a general problem-solving tool called limit theory. This is an advanced version of
asymptotic analysis of discrete problems when some finite parameter tends to infinity. We …

In this paper we give a proof of the Miklós–Manickam–Singhi (MMS) conjecture for some
partial geometries. Specifically, we give a condition on partial geometries which implies that …

Abstract Let [n]={1, 2,⋯, n}. Let [n] k be the family of all subsets of [n] of size k. Define a real-
valued weight function w on the set [n] k such that∑ X∈[n] kw (X)≥ 0. Let U n, t, k be the set …

Abstract Let n={1, 2,\dots, n\} n= 1, 2,⋯, n. For each i ∈ ki∈ k and j ∈ nj∈ n, let w_ i (j) wi (j)
be a real number. Suppose that ∑ _ i ∈ k, j ∈ n w_ i (j) ≥ 0∑ i∈ k, j∈ n wi (j)≥ 0 …

More than twenty-five years ago, Manickam, Miklos, and Singhi conjectured that for positive
integers $ n, k $ with $ n\geq 4k $, every set of $ n $ real numbers with nonnegative sum has …