Let’s take a closer look at the numerical incidence properties of relations, concentrating on the assorted regularity conditions defined in the article on Relation Theory.
For example, has the property of being
if and only if the cardinality of the local flag
is equal to
for all
in
coded in symbols, if and only if
for all
in
In like fashion, one may define the numerical incidence properties
and so on. For ease of reference, a few of these definitions are recorded below.
Clearly, if any relation is on one of its domains
and also
on the same domain, then it must be
on that domain, in short,
at
For example, let and
and consider the dyadic relation
that is bigraphed below:
![]() |
(38) |
We observe that is 3-regular at
and 1-regular at
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