9 citations · 28 across the 17 of their papers we have counts for
17 papers
Both directions of Fuglede's conjecture fail in dimension two
Tao Zhang
Fuglede's conjecture asserts that a measurable set of positive and finite measure is spectral if and only if it tiles Euclidean space by translations. Counterexamples are known in…
A Delsarte Linear Programming Approach to the Erdős--Falconer Distance Problem over Finite Fields
Tao Zhang
We introduce a Delsarte linear programming approach to the finite field Erdős--Falconer distance problem. Let \(q\) be an odd prime power, let \(n\) be even, and let \(Q\) be a non…
Additive structures imply more distances in
Daewoong Cheong, Gennian Ge, Doowon Koh +3
For a set , the distance set is defined as , where denotes the stand…
New results on sparse representations in unions of orthonormal bases
Tao Zhang, Gennian Ge
The problem of sparse representation has significant applications in signal processing. The spark of a dictionary plays a crucial role in the study of sparse representation. Donoho…
Fuglede's conjecture holds in
Tao Zhang
Fuglede's conjecture states that for a subset of a locally compact abelian group with positive and finite Haar measure, there exists a subset of the dual group of which…
A polynomial resultant approach to algebraic constructions of extremal graphs
Tao Zhang, Zixiang Xu, Gennian Ge
The Turán problem asks for the largest number of edges ex in an -vertex graph not containing a fixed forbidden subgraph , which is one of the most important problems i…
New lower bounds for the Turán density of
Tao Zhang, Gennian Ge
Let be an -uniform hypergraph. The Turán number is the maximum number of edges in an -vertex -free -uniform hypergrap…
Color isomorphic even cycles and a related Ramsey problem
Zixiang Xu, Tao Zhang, Yifan Jing +1
In this paper, we first study a new extremal problem recently posed by Conlon and Tyomkyn~(arXiv: 2002.00921). Given a graph and an integer , let be…
On the Turán number of 1-subdivision of
Tao Zhang, Zixiang Xu, Gennian Ge
For a graph , the 1-subdivision of , denoted by , is the graph obtained by replacing the edges of by internally disjoint paths of length 2. Recently, Conlon, Janzer a…
Some New Results on Splitter Sets
Zuo Ye, Tao Zhang, Xiande Zhang +1
Splitter sets have been widely studied due to their applications in flash memories, and their close relations with lattice tilings and conflict avoiding codes. In this paper, we gi…
New lower bounds for partial -parallelisms
Tao Zhang, Yue Zhou
Due to the applications in network coding, subspace codes and designs have received many attentions. Suppose that and is an -dimensional space over the finite…
3-uniform hypergraphs with few Berge paths of length three between any two vertices
Tao Zhang, Zixiang Xu, Gennian Ge
Recently, Berge theta hypergraphs have received special attention due to the similarity with Berge even cycles. Let -uniform Berge theta hypergraph be the -u…
Some tight lower bounds for Turán problems via constructions of multi-hypergraphs
Zixiang Xu, Tao Zhang, Gennian Ge
Recently, several hypergraph Turán problems were solved by the powerful random algebraic method. However, the random algebraic method usually requires some parameters to be very la…
Some extremal results on K_{s,t}-free graphs
Tao Zhang, Gennian Ge
For graphs and , let be the maximum possible number of copies of in an -free graph on vertices. The study of this function, which generalizes t…
On the nonexistence of linear perfect Lee codes
Tao Zhang, Yue Zhou
In 1968, Golomb and Welch conjectured that there does not exist perfect Lee code in with radius and dimension . Besides its own interest in coding t…
Invertible binary matrix with maximum number of -by- invertible submatrices
Yiwei Zhang, Tao Zhang, Xin Wang +1
The problem is related to all-or-nothing transforms (AONT) suggested by Rivest as a preprocessing for encrypting data with a block cipher. Since then there have been various applic…
Proof of Sun's conjectures on super congruences and the divisibility of certain binomial sums
Guo-Shuai Mao, Tao Zhang
In this paper, we prove two conjectures of Z.-W. Sun: $$2n\binom{2n}n\big|\sum_{k=0}^{n-1}(3k+1)\binom{2k}k^3{16}^{n-1-k}\ \mbox{for}\ \mbox{all}\ n=2,3,\cdots,$$ and $$\sum_{k=0}^…