P. Němec

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20042026

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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…