arXiv subjects

Nguyen Trong Tuan

Publications and source records attributed to Nguyen Trong Tuan.

3 recordsLinked to original sources

arXiv2026

Characterization of Maximal Left-Compressed Intersecting Families Generated by a Single Generator

In this paper, we focus on left-compressed families $\mathcal{F}(\mathcal{G})$ generated by a family of sets $\mathcal{G}$. We establish a necessary and sufficient condition on $\mathcal{G}$ under which $\mathcal{F}(\mathcal{G})$ is intersecting. We then introduce a construction of maximal left-compressed intersecting families $\mathcal{F}_G$ from a single generator by adding suitable sets not containing $1$ to $F(G)$. From this, we derive several estimates for the size of $\mathcal{F}_G$.

math.CO↗

arXiv2022

Short injective proofs of the Erdős-Ko-Rado and Hilton-Milner Theorem: A canonical partition of shifted intersecting set systems

We give a canonical partition of shifted intersecting set systems, from which one can obtain unified and elementary proofs of the Erdős-Ko-Rado and Hilton-Milner Theorem, as well as a characterization of maximal shifted $k$-uniform intersecting set systems over $[n]$.

math.CO↗

arXiv2019

On perfect order subsets in finite groups

If $G$ is a finite group and $x\in G$ then the set of all elements of $G$ having the same order as $x$ is called {\em an order subset of $G$ determined by $x$} (see [2]). We say that $G$ is a {\em group with perfect order subsets} or briefly, $G$ is a {\em $POS$-group} if the number of elements in each order subset of $G$ is a divisor of $|G|$. In this paper we prove that for any $n\geq 4$, the symmetric group $S_n$ is not $POS$-group. This gives the positive answer to one of two questions rising from Conjecture 5.2 in [3].

math.GR↗