Hui-Qin Cao

activity

20052022

most citedSome congruences for trinomial coefficients

5 citations · 14 across the 12 of their papers we have counts for

collaborators

12 papers

math.RA2022

The Moore-Penrose Inverses of Clifford Algebra $C ℓ_{2}$

Rong lan Zheng, Wen sheng Cao, Hui hui Cao

In this paper, we introduce a ring isomorphism between the Clifford algebra $C ℓ_{2}$ and a ring of matrices, and represent the elements in $C ℓ_{2}$ by real matrices. By such a ri…

math.RA2022

The Moore-Penrose Inverses of Clifford Algebra $C ℓ_{1, 2}$

Wensheng Cao, Ronglan Zheng, Huihui Cao

In this paper, we introduce a ring isomorphism between the Clifford algebra $C ℓ_{1, 2}$ and a ring of matrices. By such a ring isomorphism, we introduce the concept of the Moore-…

math.AG2022

The Euler's formula and root formula of Clifford Algebra Cl2

Wensheng Cao, Huihui Cao, Ronglan Zheng

In this paper, we express Euler's formula and De Moivre's formula for Clifford algebra Cl2 and find nth roots of an element in Clifford algebra Cl2.

math.NT2018★ 1 cited

Congruences for Apéry numbers $β_{n} = \sum_{k = 0}^{n} (k n)^{2} (k n + k)$

Hui-Qin Cao, Yuri Matiyasevich, Zhi-Wei Sun

In this paper we establish some congruences involving the Apéry numbers $β_{n} = \sum_{k = 0}^{n} (k n)^{2} (k n + k)$ $(n = 0, 1, 2, \dots)$ . For example, we show that $$\sum_{k=0…

math.NT2015

A Stern-type congruence for the Schroder numbers

Hui-Qin Cao, Hao Pan

For the Schröder number $S_{n} = k = 0 \sum n (k n) (k n + k) \frac{1}{k + 1},$ we prove that $S_{n + 2^{α}} \equiv S_{n} + 2^{α + 1} (mod 2^{α + 2}),$ where $n \geq 1$ and $α \geq 1$ .

math.CO2010★ 5 cited

On a sumset problem for integers

Shan-Shan Du, Hui-Qin Cao, Zhi-Wei Sun

Let $A$ be a finite set of integers. We show that if $k$ is a prime power or a product of two distinct primes then $∣ A + k \cdot A ∣ \geq (k + 1) ∣ A ∣ - ⌈ k (k + 2) /4 ⌉$ provided $|A|\…