Philipp Heering

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20232026

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8 papers · 1 filter

math.CO2026

A note on the chromatic number of Kneser graphs on chambers of projective planes and incidence-free sets

Philipp Heering, Klaus Metsch, Vladislav Taranchuk +1

Let $D = (P, B)$ be a symmetric $(v, k, λ)$ -design and let $(X, Y)$ be an equinumerous incidence-free pair, with $X \subseteq P$ and $Y \subseteq B$ …

math.CO2026

Cocliques in the Kneser graph on $(n - 1, n)$ -flags of PG $(2 n, q)$

Philipp Heering

In the finite projective space PG $(2 n, q)$ we consider flags of type $(n - 1, n)$ , that is, pairs $(A, B)$ consisting of an $(n - 1)$ -space $A$ and an $n$ -space $B$ that are incident. Two…

math.CO2025

Line-parallelisms of PG $(n, 2)$ from Preparata-like codes

Philipp Heering, Vladislav Taranchuk

Partitions of the binary linear Hamming code into Preparata-like codes are known to induce line-parallelisms of PG $(n, 2)$ . In this paper, we show that if $P$ is any Preparata-like…

math.CO2025

On the Erdős-Ko-Rado problem of flags with type ${1, n - 3}$ of finite sets

Philipp Heering

A flag of a finite set $S$ is a set $f$ of non-empty, proper subsets of $S$ , such that $X \subseteq Y$ or $Y \subseteq X$ for all $X, Y \in f$ . Two flags $f_{1}$ and $f_{2}$ of $S$ are opp…

math.CO2025

The largest sets of non-opposite chambers in spherical buildings of type $B$

Jan De Beule, Philipp Heering, Sam Mattheus +1

The investigation into large families of non-opposite flags in finite spherical buildings has been a recent addition to a long line of research in extremal combinatorics, extending…

math.CO2024

Maximum Erdős-Ko-Rado sets of chambers and their antidesigns in vector-spaces of even dimension

Philipp Heering, Jesse Lansdown, Klaus Metsch

A chamber of the vector space $F_{q}^{n}$ is a set ${S_{1}, \dots, S_{n - 1}}$ of subspaces of $F_{q}^{n}$ where $S_{1} \subset S_{2} \subset \dots \subset S_{n - 1}$ and $\dim(S_i)…

math.CO2024

On the largest independent sets in the Kneser graph on chambers of PG(4,q)

Philipp Heering

Let $Γ_{4}$ be the graph whose vertices are the chambers of the finite projective $4$ -space PG(4,q), with two vertices being adjacent if the corresponding chambers are in general pos…

math.CO2023

Maximal cocliques and the chromatic number of the Kneser graph on chambers of PG $(3, q)$

Philipp Heering, Klaus Metsch

Let $Γ$ be the graph whose vertices are the chambers of the finite projective $3$ -space PG $(3, q)$ , with two vertices being adjacent if and only if the corresponding chambers are in…

A note on the chromatic number of Kneser graphs on chambers of projective planes and incidence-free sets

Cocliques in the Kneser graph on (n−1,n)-flags of PG(2n,q)

Line-parallelisms of PG(n,2) from Preparata-like codes

On the Erdős-Ko-Rado problem of flags with type {1,n−3} of finite sets

The largest sets of non-opposite chambers in spherical buildings of type B

Maximum Erdős-Ko-Rado sets of chambers and their antidesigns in vector-spaces of even dimension

On the largest independent sets in the Kneser graph on chambers of PG(4,q)

Maximal cocliques and the chromatic number of the Kneser graph on chambers of PG(3,q)

Cocliques in the Kneser graph on $(n - 1, n)$ -flags of PG $(2 n, q)$

Line-parallelisms of PG $(n, 2)$ from Preparata-like codes

On the Erdős-Ko-Rado problem of flags with type ${1, n - 3}$ of finite sets

The largest sets of non-opposite chambers in spherical buildings of type $B$

Maximal cocliques and the chromatic number of the Kneser graph on chambers of PG $(3, q)$