Rongzhong Xiao

collaborators

6 papers

math.GR2026

Equational theories of flat semirings $S (W)$

Zidong Gao, Yilin Zhou

We study the finite basis problem for flat semirings of the form $S (W)$ , where $W$ is a nonempty set of nonempty words, possibly infinite. We prove that $S (W)$ is finitely based if…

math.DS2026

A three-dimensional corner configuration involving the Omega function

Zhuowen Guo, Rongzhong Xiao, Shuhao Zhang

Let $Ω (n)$ denote the number of prime factors of $n$ , counted with multiplicity. We prove that if $A \subset N^{3}$ has positive upper Banach density, then there are $(x,y,z)\…

math.CO2026

An affirmative answer to Owings's sumset question

Wen Huang, Zhengxing Lian, Song Shao +3

We give an affirmative answer to Owings's sumset question: for any $2$ -coloring of natural numbers, there is an infinite $B \subseteq N$ such that $B + B$ is monochromatic. Mo…

math.DS2024

Some ergodic theorems involving Omega function and their applications

Rongzhong Xiao

In this paper, we build some ergodic theorems involving function $Ω$ , where $Ω (n)$ denotes the number of prime factors of a natural number $n$ counted with multiplicities. As a com…

math.CO2024

Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers

Wen Huang, Song Shao, Tianyi Tao +2

In this paper we prove that for any finite coloring of N there are lambda,rho in N such that infinitely many pairs (x,y),(u,v) in N^2 satisfy the sets {lambda x, lambda y, x y, lam…

math.CO2024

Monochromatic polynomial sumset structures on $N$

Zhengxing Lian, Rongzhong Xiao

In the paper, we search for monochromatic infinite additive structures involving polynomials over $N$ . It is proved that for any $r \in N$ , any two distinct natura…

Equational theories of flat semirings S(W)