I. Hetman

collaborators

10 papers

math.CO2026

Steiner systems $S (2, 6, 226)$ and $S (2, 6, 441)$ exist

Taras Banakh, Ivan Hetman, Alex Ravsky

Via computer search, we found seven non-isomorphic $1$ -rotational Steiner systems $S (2, 6, 226)$ and six point-transitive Steiner systems $S (2, 6, 441)$ , resolving two of $29$ previous…

math.CO2026

There exist Steiner systems $S (2, 7, 505)$ , $S (2, 7, 589)$ , and $S (2, 8, 624)$

Ivan Hetman

In this note two Steiner systems $S (2, 7, 505)$ , two Steiner systems $S (2, 7, 589)$ , and ten Steiner systems $S (2, 8, 624)$ are presented. This resolves two of $21$ undecided cases for b…

math.CO2026

There exist Steiner systems $S (2, 8, 225)$ and $S (2, 9, 289)$

Ivan Hetman

In this note six Steiner systems $S (2, 8, 225)$ and four Steiner systems $S (2, 9, 289)$ are presented. This resolves two of $129$ undecided cases for block designs with block length $8…

math.CO2026

Existence of $S (2, 9, 369)$ , new unitals of order $6$ and other Steiner systems with block length $\geq 7$

Ivan Hetman

Whereas Steiner systems $S (2, k, v)$ with block length $k \leq 5$ have large amount of examples and the existence is established for all admissible $v$ , for $k \geq 6$ only few examples…

math.CO2025

New Steiner systems $S (2, 6, v)$ with block length 6

Taras Banakh, Ivan Hetman, Alex Ravsky

In this paper various Steiner systems $S (2, k, v)$ for $k = 6$ are collected and enumerated for specific constructions. In particular, two earlier unknown types of $1$ -rotational des…

math.HO2025

Linear Geometry: flats, ranks, regularity, parallelity

Taras Banakh, Ivan Hetman, Alex Ravsky +1

Linear Geometry describes geometric properties that depend on the fundamental notion of a line. In this paper we survey basic notions and results of Linear Geomery that depend on t…

Steiner systems S(2,6,226) and S(2,6,441) exist

There exist Steiner systems S(2,7,505), S(2,7,589), and S(2,8,624)

There exist Steiner systems S(2,8,225) and S(2,9,289)

Existence of S(2,9,369), new unitals of order 6 and other Steiner systems with block length ≥7

New Steiner systems S(2,6,v) with block length 6

Linear Geometry: flats, ranks, regularity, parallelity

Steiner systems $S (2, 6, 226)$ and $S (2, 6, 441)$ exist

There exist Steiner systems $S (2, 7, 505)$ , $S (2, 7, 589)$ , and $S (2, 8, 624)$

There exist Steiner systems $S (2, 8, 225)$ and $S (2, 9, 289)$

Existence of $S (2, 9, 369)$ , new unitals of order $6$ and other Steiner systems with block length $\geq 7$

New Steiner systems $S (2, 6, v)$ with block length 6