252 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
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
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 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
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
Boolean degree 1 functions on some classical association schemes
We investigate Boolean degree 1 functions for several classical association
schemes, including Johnson graphs, Grassmann graphs, graphs from polar spaces,
and bilinear forms graphs, as well as some other domains such as multislices
(Young subgroups of the symmetric group). In some settings, Boolean degree 1
functions are also known as \textit{completely regular strength 0 codes of
covering radius 1}, \textit{Cameron--Liebler line classes}, and \textit{tight
sets}.
We classify all Boolean degree functions on the multislice. On the
Grassmann scheme we show that all Boolean degree functions are
trivial for , and , and that
for general , the problem can be reduced to classifying all Boolean degree
functions on . We also consider polar spaces and the bilinear
forms graphs, giving evidence that all Boolean degree functions are trivial
for appropriate choices of the parameters.Comment: 22 pages; accepted by JCTA; corrected Conjecture 6.
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