On the Erd\H {o} s--Ginzburg--Ziv Problem in large dimension
L Sauermann, D Zakharov - arXiv preprint arXiv:2302.14737, 2023 - arxiv.org
The Erd\H {o} s--Ginzburg--Ziv Problem is a classical extremal problem in discrete geometry.
Given $ m $ and $ n $, the problem asks about the smallest number $ s $ such that among …
Given $ m $ and $ n $, the problem asks about the smallest number $ s $ such that among …
New applications of the polynomial method: the cap set conjecture and beyond
J Grochow - Bulletin of the American Mathematical Society, 2019 - ams.org
The cap set problem asks how large can a subset of $(\mathbb {Z}/3\mathbb {Z})^ n $ be and
contain no lines or, more generally, how can large a subset of $(\mathbb {Z}/p\mathbb {Z}) …
contain no lines or, more generally, how can large a subset of $(\mathbb {Z}/p\mathbb {Z}) …
Tensors Ranks and the Fine-Grained Complexity of Dynamic Programming
Generalizing work of K\" unnemann, Paturi, and Schneider [ICALP 2017], we study a wide
class of high-dimensional dynamic programming (DP) problems in which one must find the …
class of high-dimensional dynamic programming (DP) problems in which one must find the …
Variety membership testing, algebraic natural proofs, and geometric complexity theory
We study the variety membership testing problem in the case when the variety is given as an
orbit closure and the ambient space is the set of all 3-tensors. The first variety that we …
orbit closure and the ambient space is the set of all 3-tensors. The first variety that we …
On the orbit closure containment problem and slice rank of tensors
We consider the orbit closure containment problem, which, for a given vector and a group
orbit, asks if the vector is contained in the closure of the group orbit. Recently, many …
orbit, asks if the vector is contained in the closure of the group orbit. Recently, many …
On the size of subsets of without p distinct elements summing to zero
L Sauermann - Israel Journal of Mathematics, 2021 - Springer
Let us fix a prime p. The Erdős-Ginzburg-Ziv problem asks for the minimum integer s such
that any collection of s points in the lattice ℤ n contains p points whose centroid is also a …
that any collection of s points in the lattice ℤ n contains p points whose centroid is also a …
Solving linear equations in a vector space over a finite field
M Mimura, N Tokushige - Discrete Mathematics, 2021 - Elsevier
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Sharp bounds for rainbow matchings in hypergraphs
Suppose we are given matchings $ M_1,...., M_N $ of size $ t $ in some $ r $-uniform
hypergraph, and let us think of each matching having a different color. How large does $ N …
hypergraph, and let us think of each matching having a different color. How large does $ N …
[HTML][HTML] On subsets of the hypercube with prescribed Hamming distances
A celebrated theorem of Kleitman in extremal combinatorics states that a collection of binary
vectors in {0, 1} n with diameter d has cardinality at most that of a Hamming ball of radius …
vectors in {0, 1} n with diameter d has cardinality at most that of a Hamming ball of radius …
A polynomial bound for the arithmetic k-cycle removal lemma in vector spaces
For each k≥ 3, Green proved an arithmetic k-cycle removal lemma for any abelian group G.
The best known bounds relating the parameters in the lemma for general G are of tower …
The best known bounds relating the parameters in the lemma for general G are of tower …