T. Kepka

activity

20042026

collaborators

6 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 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.RA2023

Congruence-simple matrix semirings

Vítězslav Kala, Tomáš Kepka, Miroslav Korbelář

It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semirin…

math.RA2022

Congruence-simple multiplicatively idempotent semirings

Tomáš Kepka, Miroslav Korbelář, Günter Landsmann

Let $S$ be a multiplicatively idempotent congruence-simple semiring. We show that $∣ S ∣ = 2$ if $S$ has a multiplicatively absorbing element. We also prove that if $S$ is finite then…

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…