P. Němec

collaborators

3 papers

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 BatÃ kovÃ¡, TomÃ¡Å¡ J. Kepka, Petr C. NÄmec

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 ErdÅs

Barbora BatÃkovÃ¡, TomÃ¡Å¡ J. Kepka, Petr C. NÄmec

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…

Note as to size-minimal hypercompletly separating systems

Size-minimal combinatorial designs of staircase type

Another inequality inspired by ErdÅs

Another inequality inspired by ErdÅs