2 research outputs found
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.