I. Hetman

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20112026

most citedLinear Geometry: flats, ranks, regularity, parallelity

1 citations · 1 across the 11 of their papers we have counts for

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math.CO2025

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

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.CO2025

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.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.CO2025

Enumerations of 1-rotational Steiner systems

Ivan Hetman, Taras Banakh, Alex Ravsky

In this paper new $1$ -rotational 2-Steiner systems for different admissible $v, k$ pairs are introduced. In particular, $1$ -rotational unitals of order $4$ are enumerated.

math.CO2025

Point-transitive and 1-rotational unitals of order 5

Ivan Hetman, Taras Banakh, Alex Ravsky

In this paper we introduce enumeration of unitals of order $5$ , which are also Steiner systems $S (2, 6, 126)$ , where automorphism group acts transitively and effectively on points or…

math.CO2025

Point-transitive Steiner systems S(2,6,111/121/126), S(2,7,169/175)

Ivan Hetman

In this paper new Steiner systems $S (2, 6, 111)$ , $S (2, 6, 121)$ , $S (2, 6, 126)$ , $S (2, 7, 169)$ , $S (2, 7, 175)$ and possibly others with point-transitive (commutative except $S (2, 6, 111)$ ca…

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

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

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

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

Enumerations of 1-rotational Steiner systems

Point-transitive and 1-rotational unitals of order 5

Point-transitive Steiner systems S(2,6,111/121/126), S(2,7,169/175)

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

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

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

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