The Gowers norm in the testing of Boolean functions by Chen, Victor Yen-Wen

Get full text

Dimension-Free Bounds for the Union-Closed Sets Conjecture by Lei Yu

Get full text

Randomised algorithms for low temperature spin systems by Stewart, J

“…Spin systems provide a framework for sampling and counting problems in computer science, graph homomorphism problems in combinatorics, and phase transition phenomena in statistical physics. …”

A note on the Ramsey number for cycle with respect to multiple copies of wheels by I Wayan Sudarsana

Get full text

Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs without Theta Graphs Θ_2,1,2 by Donghan Zhang

Get full text

Algorithms and Algorithmic Barriers in High-Dimensional Statistics and Random Combinatorial Structures by Kizildag, Eren C.

“…Our hardness results for the stable algorithms are based on Ramsey Theory from extremal combinatorics. To the best of our knowledge, this is the first usage of Ramsey Theory to show algorithmic hardness for models with random parameters. 2. …”
Get full text

Reliability analysis and improvement of multilevel converters by Tu, Pengfei

“…The network reliability modeling techniques, combinatorics and stochastic process, are used to model the inherent redundancy in multilevel converters. …”
Get full text
Get full text

On product sets of arithmetic progressions by Max Wenqiang Xu, Yunkun Zhou

“…In the terminology of arithmetic combinatorics, the original problem asks for the size of the product set $A.A$, where $A$ is the set $\{1,2,\dots,n\}$. …”
Get full text

New bound for Roth's theorem with generalized coefficients by Cédric Pilatte

“…It is the first non-trivial case of Szemerédi's theorem (which is the generalization from 3 to arbitrary $k$), and as such has played an absolutely central role in additive combinatorics. Surprisingly, given the simplicity of the statement, obtaining upper and lower bounds that are reasonably close to each other has turned out to be a very hard problem. …”
Get full text

New lower bounds for cap sets by Fred Tyrrell

“…One of the best known problems in additive combinatorics, the cap set problem, asks how large a subset of $\mathbb F_3^n$ can be if it contains no non-trivial solutions to the equation $x+y+z=0$. …”
Get full text

From Permutation Patterns to the Periodic Table by Saeid Alikhani, Maryam Safazadeh

“…Pudwell, From Permutation Patterns to the Periodic Table, Notices of the American Mathematical Society, 67 994–1001.))Abstract: Permutation patterns is a burgeoning area of research with roots in enumerative combinatorics and theoretical computer science. This article first presents a brief overview of pattern avoidance and a survey of enumeration results that are standard knowledge within the field. …”
Get full text

Excluding affine configurations over a finite field by Dion Gijswijt

“…In 2016 a remarkable development took place in additive combinatorics, when Ernie Croot, Seva Lev and Péter Pál Pach posted a paper to arXiv using the polynomial method to obtain an exponential upper bound for the density of a subset of $\mathbb F_4^n$ that does not contain an arithmetic progression of length 3, and very shortly afterwards, Jordan Ellenberg and the author of this paper modified the proof to obtain a similar upper bound for $\mathbb F_3^n$, thereby obtaining the correct form for the upper bound in the famous cap-set problem. …”
Get full text

Faster Provable Sieving Algorithms for the Shortest Vector Problem and the Closest Vector Problem on Lattices in <i>ℓ</i>_p Norm by Priyanka Mukhopadhyay

Get full text

Forbidden intersection problems for families of linear maps by David Ellis, Guy Kindler, Noam Lifshitz

“…A central problem in extremal combinatorics is to determine the maximal size of a set system given constraints on the sizes of the sets in the system and on the sizes of their intersections. …”
Get full text

Additive energies on discrete cubes by Jaume de Dios Pont, Rachel Greenfeld, Paata Ivanisvili, Jos\'e Madrid

“…One definition of additive combinatorics is that it is the study of subsets of (usually Abelian) groups. …”
Get full text

Geometric rank of tensors and subrank of matrix multiplication by Swastik Kopparty, Guy Moshkovitz, Jeroen Zuiddam

“…Since this paper first appeared as a preprint, the notion of geometric rank has played an important role in a central problem of additive combinatorics, which is to relate analytic rank to partition rank (where the rank-1 tensors of degree $d$ are those of the form $UV$, where $U$ and $V$ depend on disjoint sets of variables). …”
Get full text

Quantitative bounds for the $U^4$-inverse theorem over low characteristic finite fields by Jonathan Tidor

“…The $U^k$ norms play an important role in additive combinatorics because they lead to a useful definition of quasirandomness for subsets of finite Abelian groups. …”
Get full text

Hypergraphs with infinitely many extremal constructions by Jianfeng Hou, Heng Li, Xizhi Liu, Dhruv Mubayi, Yixiao Zhang

“…This is one of the most famous open problems in extremal combinatorics. It is conjectured that the extremal density is 5/9, but a sign that the conjecture is hard is that if the conjecture is true, the example just presented is not _the_ extremal example, but merely _an_ extremal example, as it is now known that there is an infinite family of 3-uniform hypergraphs with no cliques of size 4 and with asymptotic density 5/9. …”
Get full text

Gowers norms for automatic sequences by Jakub Byszewski, Jakub Konieczny, Clemens Müllner

“…There are several situations in additive and extremal combinatorics where it is useful to decompose an object $X$ into a "structured" part $S(X)$ and a "quasirandom" part $Q(X)$. …”
Get full text

Another Antimagic Conjecture by Rinovia Simanjuntak, Tamaro Nadeak, Fuad Yasin, Kristiana Wijaya, Nurdin Hinding, Kiki Ariyanti Sugeng

Get full text