New Non-existence Proofs for Ovoids of Hermitian Polar Spaces and Hyperbolic Quadrics

Bamberg, John; Beule, Jan De; Ihringer, Ferdinand

doi:10.1007/s00026-017-0346-0

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…One can see that a function µ satisfying the condition of Lemma 2.3 generalizes the notion of tight sets. The proof of the following lemma justifies this by showing that µ is a weighted tight set [1] and, moreover, given such a function µ one can construct a weighted set for hyperbolic quadrics of smaller rank. Lemma 2.4.…”

Section: The Proof Of Theorem 12mentioning

confidence: 78%

On tight sets of hyperbolic quadrics

Gavrilyuk¹

2019

Preprint

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We prove that the parameter x of a tight set T of a hyperbolic quadric Q + (2n + 1, q) of an odd rank n + 1 satisfies x 2 + w(w − x) ≡ 0 mod q + 1, where w is the number of points of T in any generator of Q + (2n + 1, q). As this modular equation should have an integer solution in w if such a T exists, this condition rules out roughly at least one half of all possible parameters x. It generalizes a previous result by the author and K. Metsch shown for tight sets of a hyperbolic quadric Q + (5, q) (also known as Cameron-Liebler line classes in PG(3, q)).

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Section: The Proof Of Theorem 12mentioning

confidence: 78%

On tight sets of hyperbolic quadrics

Gavrilyuk¹

2019

Preprint

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“…Our hope is that the discovery of low degree Boolean functions will help with deciding the existence of small designs. In principle, this is a feasible approach, which was investigated by the first and third author for slightly different, but also graphs derived from finite geometries in [1].…”

Section: Designs and Their Q-analogsmentioning

confidence: 99%

Degree 2 Boolean Functions on Grassmann Graphs

Beule¹,

D'haeseleer²,

Ihringer³

et al. 2022

Preprint

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We investigate Boolean degree d functions on the Grassmann Graph of k-spaces in F n q . Our focus are degree 2 functions for (n, k) = (6, 3) and (n, k) = (8, 4).We also discuss connections to the analysis of Boolean functions, regular sets/equitable bipartitions/perfect 2-colorings in graphs, q-analogs of designs, and permutation groups. In particular, this represents a natural generalization of Cameron-Liebler line classes.

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“…Proof. (Proposition 1) As in [1], write C n = j ⊥ V + ⊥ V − . and let E + and E − be the non-principal idempotents corresponding to V + and V − .…”

Section: (): V-volmentioning

confidence: 99%