arXiv subjects

P. C. Nemec

Publications and source records attributed to P. C. Nemec.

2 recordsLinked to original sources

arXiv2026

Note as to size-minimal hypercompletly separating systems

If $S$ is a non-empty finite set, $|S|=s$, then a system $\mathscr{A}$ of subsets of $S$ is a size-minimal hypercompletely separable system (i.e., for every $a\in S$ there are $A,B\in\mathscr{A}$ such that $A\cap B=\{a\}$) if and only if $|\mathscr{A}|=\left\lceil\frac{1+\sqrt{8s+1}}2\right\rceil$.

math.CO↗

arXiv2026

Note as to inclusion-minimal non-Bondy systems

Let $S$ be a finite set, $s=|S|\ge6$. Given a non-negative integer $t$, there exists an inclusion-minimal non-Bondy system $\mathscr{A}$ of size $t$ on $S$ if and only if $s+1\le t\le2s$.

math.CO↗