On the size of a maximal partial spread

1993 ◽  
Vol 3 (3) ◽  
pp. 187-191 ◽  
Author(s):  
Aart Blokhuis ◽  
Klaus Metsch
1978 ◽  
Vol 30 (03) ◽  
pp. 483-489 ◽  
Author(s):  
Gary L. Ebert

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 ∑.


1989 ◽  
Vol 36 (1-2) ◽  
pp. 37-48 ◽  
Author(s):  
Franco Eugeni ◽  
Mario Gionfriddo

10.37236/5501 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Antonio Cossidente ◽  
Francesco Pavese

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 $q^n+1$.


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

2016 ◽  
Vol 85 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Thor Martinsen ◽  
Wilfried Meidl ◽  
Pantelimon Stănică

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

2021 ◽  
Author(s):  
Muhammad Zubair ◽  
Sjoerd R Murris ◽  
Kaoru Isa ◽  
Hirotaka Onoe ◽  
Yoshinori Koshimizu ◽  
...  

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.


10.37236/251 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Frédéric Vanhove

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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