On the size of a maximal partial spread

1993 ◽  
Vol 3 (3) ◽  
pp. 187-191 ◽  
Author(s):  
Aart Blokhuis ◽  
Klaus Metsch
Keyword(s):  
Partial Spread ◽  
Maximal Partial Spread

Maximal Strictly Partial Spreads

1978 ◽  
Vol 30 (03) ◽  
pp. 483-489 ◽  
Author(s):  
Gary L. Ebert
Keyword(s):  
Projective Space ◽  
Partial Spread ◽  
3 Dimensional ◽  
Partial Spreads ◽  
Maximal Partial Spread ◽  
Dimensional Projective Space

Let ∑ = PG(3, q) denote 3-dimensional projective space over GF(q). A partial spread of ∑ is a collection W of pairwise skew lines in ∑. W is said to be maximal if it is not properly contained in any other partial spread. If every point of ∑ is contained in some line of W, then W is called a spread. Since every spread of PG(3, q) consists of q2 + 1 lines, the deficiency of a partial spread W is defined to be the number d = q2 + 1 — |W|. A maximal partial spread of ∑ which is not a spread is called a maximal strictly partial spread (msp spread) of ∑.

On the minimum number of blocks of a maximal partial spread in STS(v) and SQS(v)

1989 ◽  
Vol 36 (1-2) ◽  
pp. 37-48 ◽  
Author(s):  
Franco Eugeni ◽  
Mario Gionfriddo
Keyword(s):  
Partial Spread ◽  
Maximal Partial Spread ◽  
Minimum Number

scholarly journals Maximal Partial Spreads of Polar Spaces

10.37236/5501 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Antonio Cossidente ◽  
Francesco Pavese
Keyword(s):  
Partial Spread ◽  
Polar Spaces ◽  
Partial Spreads ◽  
Maximal Partial Spread ◽  
Classical Polar Spaces

Some constructions of maximal partial spreads of finite classical polar spaces are provided. In particular we show that, for $n \ge 1$, $\mathcal{H}(4n-1,q^2)$ has a maximal partial spread of size $q^{2n}+1$, $\mathcal{H}(4n+1,q^2)$ has a maximal partial spread of size $q^{2n+1}+1$ and, for $n \ge 2$, $\mathcal{Q}^+(4n-1,q)$, $\mathcal{Q}(4n-2,q)$, $\mathcal{W}(4n-1,q)$, $q$ even, $\mathcal{W}(4n-3,q)$, $q$ even, have a maximal partial spread of size $q^n+1$.

Counting Partial Spread Functions in Eight Variables

2011 ◽  
Vol 57 (4) ◽  
pp. 2263-2269 ◽  
Author(s):  
Philippe Langevin ◽  
Xiang-Dong Hou
Keyword(s):  
Partial Spread

scholarly journals Partial spread and vectorial generalized bent functions

2016 ◽  
Vol 85 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Thor Martinsen ◽  
Wilfried Meidl ◽  
Pantelimon Stănică
Keyword(s):  
Bent Functions ◽  
Partial Spread ◽  
Generalized Bent Functions

scholarly journals The maximum size of a partial spread in H(5,q2) is q3+1

2007 ◽  
Vol 114 (4) ◽  
pp. 761-768 ◽  
Author(s):  
J. De Beule ◽  
K. Metsch
Keyword(s):  
Maximum Size ◽  
Partial Spread

scholarly journals Divergent Whole Brain Projections from the Ventral Midbrain in Macaques

2021 ◽  
Author(s):  
Muhammad Zubair ◽  
Sjoerd R Murris ◽  
Kaoru Isa ◽  
Hirotaka Onoe ◽  
Yoshinori Koshimizu ◽  
...  
Keyword(s):  
Dopaminergic Neurons ◽  
Fluorescent Proteins ◽  
Molecular Layer ◽  
Partial Spread ◽  
Double Labeling ◽  
Ventral Midbrain ◽  
Midbrain Neurons ◽  
Highly Sensitive ◽  
Layer I ◽  
The Brain

ABSTRACT To understand the connectome of the axonal arborizations of dopaminergic midbrain neurons, we investigated the anterograde spread of highly sensitive viral tracers injected into the ventral tegmental area (VTA) and adjacent areas in 3 macaques. In 2 monkeys, injections were centered on the lateral VTA with some spread into the substantia nigra, while in one animal the injection targeted the medial VTA with partial spread into the ventro-medial thalamus. Double-labeling with antibodies against transduced fluorescent proteins (FPs) and tyrosine hydroxylase indicated that substantial portions of transduced midbrain neurons were dopaminergic. Interestingly, cortical terminals were found either homogeneously in molecular layer I, or more heterogeneously, sometimes forming patches, in the deeper laminae II–VI. In the animals with injections in lateral VTA, terminals were most dense in somatomotor cortex and the striatum. In contrast, when the medial VTA was transduced, dense terminals were found in dorsal prefrontal and temporal cortices, while projections to striatum were sparse. In all monkeys, orbitofrontal and occipito-parietal cortex received strong and weak innervation, respectively. Thus, the dopaminergic ventral midbrain sends heterogeneous projections throughout the brain. Furthermore, our results suggest the existence of subgroups in meso-dopaminergic neurons depending on their location in the primate ventral midbrain.

scholarly journals The Maximum Size of a Partial Spread in $H(4 n +1, q^2)$ is $q^{2 n +1}+1$

10.37236/251 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Frédéric Vanhove
Keyword(s):  
Maximum Size ◽  
Polar Space ◽  
Maximal Dimension ◽  
Partial Spread ◽  
Isotropic Subspaces ◽  
Hermitian Polar Space ◽  
Totally Isotropic Subspaces

We prove that in every finite Hermitian polar space of odd dimension and even maximal dimension $\rho$ of the totally isotropic subspaces, a partial spread has size at most $q^{\rho+1}+1$, where $GF(q^2)$ is the defining field. This bound is tight and is a generalisation of the result of De Beule and Metsch for the case $\rho=2$.

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