P. Němec

activity

20042026

collaborators

5 papers

math.CO2026

Note as to inclusion-minimal non-Bondy systems

T. J. Kepka, P. C. Nemec, J. D. Phillips

Let $S$ be a finite set, $s = ∣ S ∣ \geq 6$ . Given a non-negative integer $t$ , there exists an inclusion-minimal non-Bondy system $A$ of size $t$ on $S$ if and only if $s+1\le t…

math.CO2026

Note as to size-minimal hypercompletly separating systems

B. Batikova, T. J. Kepka, P. C. Nemec

If $S$ is a non-empty finite set, $∣ S ∣ = s$ , then a system $A$ of subsets of $S$ is a size-minimal hypercompletely separable system (i.e., for every $a \in S$ there are $A,B…

math.CO2025

Size-minimal combinatorial designs of staircase type

Barbora Batí ková, Tomáš J. Kepka, Petr C. Němec

Given a positive integer $n$ and a partitioning $n = r_{1} s_{1} + \dots + r_{t} s_{t}$ , $t, r_{i}, s_{i}$ positive integers, such that $r_{1} > \dots > r_{t}$ (for $t \geq 2$ ), we can write $n$ symbols $1,\dots…

math.NT2025

Another inequality inspired by Erdős

Barbora Batíková, Tomáš J. Kepka, Petr C. Němec

In our effort to find an arithmetically pure proof of the Bertrand postulate, we investigate and solve (using only elementary arithmetical methods) another less usual inequality in…

math.RA2004

Hamiltonian selfdistributive quasigroups

Dolors Herbera, Tomás Kepka, Petr Nemec

The problem of the existence of non-medial distributive hamiltonian quasigroups is solved. Translating this problem first to commutative Moufang loops with operators, then to terna…