19 research outputs found
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
The Cameron-Liebler problem for sets
Cameron-Liebler line classes and Cameron-Liebler k-classes in PG(2k+1,q) are
currently receiving a lot of attention. Links with the Erd\H{o}s-Ko-Rado
results in finite projective spaces occurred. We introduce here in this article
the similar problem on Cameron-Liebler classes of sets, and solve this problem
completely, by making links to the classical Erd\H{o}s-Ko-Rado result on sets.
We also present a characterisation theorem for the Cameron-Liebler classes of
sets
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
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 in
We study Cameron-Liebler -sets in the affine geometry, so sets of
-spaces in . This generalizes research on Cameron-Liebler
-sets in the projective geometry . Note that in algebraic
combinatorics, Cameron-Liebler -sets of correspond to
certain equitable bipartitions of the Association scheme of -spaces in
, while in the analysis of Boolean functions, they correspond
to Boolean degree functions of . We define Cameron-Liebler
-sets in by intersection properties with -spreads and
show the equivalence of several definitions. In particular, we investigate the
relationship between Cameron-Liebler -sets in and
. As a by-product, we calculate the character table of the
association scheme of affine lines. Furthermore, we characterize the smallest
examples of Cameron-Liebler -sets. This paper focuses on
for , while the case for Cameron-Liebler line classes in was already treated separately
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)
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