I. Hetman

activity

20112026

most citedLinear Geometry: flats, ranks, regularity, parallelity

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

collaborators

13 papers

math.CO2026

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

Ivan Hetman

In this note two Steiner systems $S (2, 7, 505)$ and two Steiner systems $S (2, 7, 589)$ are presented. This resolves two of $21$ undecided cases for block designs with block length $7$ ,…

math.HO2025★ 1 cited

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…

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…

math.CO2024

Steiner systems S(2,6,121/126), S(2,7,169) based on difference families

Ivan Hetman

In this paper new Steiner systems $S (2, 6, 121)$ , $S (2, 6, 126)$ , $S (2, 7, 169)$ are introduced. Also some non-existence results for line lengths $7..11$ are presented. There is no solid…

math.GT2011

Recognizing the topology of the space of closed convex subsets of a Banach space

Taras Banakh, Ivan Hetman, Katsuro Sakai

Let $X$ be a Banach space and $C o n v_{H} (X)$ be the space of non-empty closed convex subsets of $X$ , endowed with the Hausdorff metric $d_{H}$ . We prove that each connected component of…

math.FA2011

A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces

Taras Banakh, Ivan Hetman

For a Banach space $X$ by $C o n v_{H} (X)$ we denote the space of non-empty closed convex subsets of $X$ , endowed with the Hausdorff metric. We prove that for any closed convex set $C\s…

math.FA2011

A "hidden" characterization of polyhedral convex sets

Taras Banakh, Ivan Hetman

We prove that a closed convex subset $C$ of a complete linear metric space $X$ is polyhedral in its closed linear hull if and only if no infinite subset $A \subset X \ C$ ca…

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

Linear Geometry: flats, ranks, regularity, parallelity

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)

Steiner systems S(2,6,121/126), S(2,7,169) based on difference families

Recognizing the topology of the space of closed convex subsets of a Banach space

A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces

A "hidden" characterization of polyhedral convex sets

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

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