54 research outputs found
Equivalent definitions for (degree one) Cameron-Liebler classes of generators in finite classical polar spaces
In this article, we study degree one Cameron-Liebler sets of generators in
all finite classical polar spaces, which is a particular type of a
Cameron-Liebler set of generators in this polar space, [9]. These degree one
Cameron-Liebler sets are defined similar to the Boolean degree one functions,
[15]. We summarize the equivalent definitions for these sets and give a
classification result for the degree one Cameron-Liebler sets in the polar
spaces W(5,q) and Q(6,q)
Cameron-Liebler sets of k-spaces in PG(n,q)
Cameron-Liebler sets of k-spaces were introduced recently by Y. Filmus and F.
Ihringer. We list several equivalent definitions for these Cameron-Liebler
sets, by making a generalization of known results about Cameron-Liebler line
sets in PG(n, q) and Cameron-Liebler sets of k-spaces in PG(2k + 1, q). We also
present a classification result
Regular ovoids and Cameron-Liebler sets of generators in polar spaces
Cameron-Liebler sets of generators in polar spaces were introduced a few
years ago as natural generalisations of the Cameron-Liebler sets of subspaces
in projective spaces. In this article we present the first two constructions of
non-trivial Cameron-Liebler sets of generators in polar spaces. Also regular
m-ovoids of k-spaces are introduced as a generalization of m-ovoids of polar
spaces. They are used in one of the aforementioned constructions of
Cameron-Liebler sets
Cameron-Liebler sets of k-spaces in PG(n,q)
Cameron-Liebler sets of k-spaces were introduced recently by Y. Filmus and F.
Ihringer. We list several equivalent definitions for these Cameron-Liebler
sets, by making a generalization of known results about Cameron-Liebler line
sets in PG(n, q) and Cameron-Liebler sets of k-spaces in PG(2k + 1, q). We also
present a classification result
Cameron-Liebler sets of k-spaces in PG(n,q)
Cameron-Liebler sets of k-spaces were introduced recently in Filmus and Ihringer (J Combin Theory Ser A, 2019). We list several equivalent definitions for these Cameron-Liebler sets, by making a generalization of known results about Cameron-Liebler line sets in PG(n,q) and Cameron-Liebler sets of k-spaces in PG(2k+1,q). We also present some classification results
A combinatorial characterisation of embedded polar spaces
Some classical polar spaces admit polar spaces of the same rank as embedded
polar spaces (often arisen as the intersection of the polar space with a
non-tangent hyperplane). In this article we look at sets of generators that
behave combinatorially as the set of generators of such an embedded polar
space, and we prove that they are the set of generators of an embedded polar
space
On the smallest non-trivial tight sets in Hermitian polar spaces
We show that an x-tight set of the Hermitian polar spaces H(4; q(2)) and H(6; q(2)) respectively, is the union of x disjoint generators of the polar space provided that x is small compared to q. For H(4; q(2)) we need the bound x < q + 1 and we can show that this bound is sharp
Cameron-Liebler sets for maximal totally isotropic flats in classical affine spaces
Let be the -dimensional classical affine space
with parameter over a -element finite field , and be the set of all maximal totally isotropic flats in
. In this paper, we discuss Cameron-Liebler sets in
, obtain several equivalent definitions and present some
classification results.Comment: 25 page
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