F. Ihringer

Optimally pseudorandom $K_{4}$ -free graphs

Jie Han, Ferdinand Ihringer, Hendrik Van Maldeghem

We show that optimally pseudorandom $K_{4}$ -free graphs of order $n$ and degree $d = Θ (n^{4/5})$ exist by constructing a graph in the split Cayley hexagon, matching the known upper b…

An improved algebraic construction for Ramsey numbers

Ferdinand Ihringer, Sam Mattheus

We provide an explicit algebraic construction showing that, uniformly for integers $3 \leq s \leq t$ , as $t \to \infty$ , \[ R( s,t ) \geq t^{(1-o(1)) \log s / \log(\log s + 1) }. \…

Structure of $t$ -Intersecting Families of Vector Spaces

Ferdinand Ihringer, Andrey Kupavskii

We study $t$ -intersecting and $t$ -cross-intersecting families of $k$ -dimensional subspaces in finite vector spaces of dimension $n$ . We show that all large $t$ -intersecting familie…

On the construction of large local arcs

Ferdinand Ihringer, Yue Zhou

Motivated by the construction of optimal locally repairable codes, we introduce the new finite geometric concept of a \emph{local arc} which is defined as a collection $\mathcal{S}…

Skirting the $n$ -tuples

Sam Adriaensen, Ferdinand Ihringer, William J. Martin +1

Let $n \geq 2$ and $q \geq 2$ be given. The set $X = Z_{q}^{n}$ is a metric space of diameter $n$ under the Hamming metric $d (\cdot, \cdot)$ . We seek a smallest set $S \subseteq X$ t…

Bijection Between Point-Hyperplane Anti-Flags of $V (n, 2)$ and Non-Singular Points of $O^{+} (2 n, 2)$

Ferdinand Ihringer, Antonio Pasini

We give a bijection between the point-hyperplane antiflags of $V (n, 2)$ and the nonsingular points of $V (2 n, 2)$ with respect to a hyperbolic quadric. With the help of…

Design switching on graphs

Ferdinand Ihringer, Robin Simoens

We show that each (r, lambda)-design yields a class of switching methods that can be used to produce cospectral graphs. We use this to explain several specific switching methods su…

New Constructions of Distance-Biregular Graphs

Blas Fernández, Ferdinand Ihringer, Sabrina Lato +1

We construct a new family of distance-biregular graphs related to hyperovals and a new sporadic example of a distance-biregular graph related to Mathon's perp system. The infinite…

math.GT2025

Small genus, small index critical points of the systole function

Ni An, Ferdinand Ihringer, Ingrid Irmer

In this paper the index of a family of critical points of the systole function on Teichmüller space is calculated. The members of this family are interesting in that their existenc…

math.CO2025★ 1 cited

On the twin-width of near-regular graphs

Irene Heinrich, Ferdinand Ihringer, Simon Raßmann +1

Twin-width is a recently introduced graph parameter based on the repeated contraction of near-twins. It has shown remarkable utility in algorithmic and structural graph theory, as…

Intersecting Families of Spanning Trees

Peter Frankl, Glenn Hurlbert, Ferdinand Ihringer +4

A family $F$ of spanning trees of the complete graph on $n$ vertices $K_{n}$ is \emph{ $t$ -intersecting} if any two members have a forest on $t$ edges in common. We prove an…

math.CO2024

A Survey of Cameron-Liebler Sets and Low Degree Boolean Functions in Grassmann Graphs

Ferdinand Ihringer

We survey results for Cameron-Liebler sets and low degree Boolean functions for Hamming graphs, Johnson graphs and Grassmann graphs from the point of view of association schemes. T…

math.CO2024

New bounds and constructions for large partial $m$ -ovoids and related structures

John Bamberg, Anurag Bishnoi, Ferdinand Ihringer +1

We use $p$ -rank bounds on partial ovoids and the classical bounds on Ramsey numbers to obtain upper bounds on the size of partial $m$ -ovoids in finite classical polar spaces. These…

math.CO2024

A common generalization of hypercube partitions and ovoids in polar spaces

Jozefien D'haeseleer, Ferdinand Ihringer, Kai-Uwe Schmidt

We investigate what we call generalized ovoids, that is families of totally isotropic subspaces of finite classical polar spaces such that each maximal totally isotropic subspace c…

Ratio bound (Lovász number) versus inertia bound

Ferdinand Ihringer

Matthew Kwan and Yuval Wigderson showed that for an infinite family of graphs, the Lovász number gives an upper bound of $O (n^{3/4})$ for the size of an independent set (where $n$ …

The classification of Boolean degree $1$ functions in high-dimensional finite vector spaces

Ferdinand Ihringer

We classify the Boolean degree $1$ functions of $k$ -spaces in a vector space of dimension $n$ (also known as Cameron-Liebler classes) over the field with $q$ elements for $n \geq n…

Regular sets of lines in rank 3 polar spaces

Ferdinand Ihringer, Morgan Rodgers

There are 6 families of finite polar spaces of rank $3$ . The set of lines in a rank $3$ polar space form a rank $5$ association scheme. We determine the regular sets of minimal siz…

Local recognition of the point graphs of some Lie incidence geometries

Ferdinand Ihringer, Paulien Jansen, Linde Lambrecht +4

Given a finite Lie incidence geometry which is either a polar space of rank at least $3$ or a strong parapolar space of symplectic rank at least $4$ and diameter at most $4$ , or th…

On MSR Subspace Families of Lines

Ferdinand Ihringer

A minimum storage regenerating (MSR) subspace family of $F_{q}^{2 m}$ is a set $S$ of $m$ -spaces in $F_{q}^{2 m}$ such that for any $m$ -space $S$ in $\mathcal…