Assistance with Notation in the Paper Entitled: "Search Through Systematic Set Enumeration" So I'm reading &quot;Search Through Systematic Set Enumeration&quot; by Ron Rymon (currently available online for free.  I'm having a problem with the notation in the following definition presented bellow:

The
Set-Enumeration
(SE)-tree
is
a
vehicle for representing
and/or
enumerating sets
in
a best-first fashion.
The
complete
SE-tree
systematically enumerates
elements
of
a
power-set using a
pre-imposed
order
on
the
underlying set
of
elements.
In
problems
where
the
search
space
is
a
subset
of
that
power-set
that
is
(or
can
be)
closed
under
set-inclusion,
the
SE-tree
induces
a
complete
irredundant
search technique.
Let
E
be
the
underlying
set
of
elements.
We
first index
E's
elements
using
a
one-to-one
function
ind: E -&gt; $ \mathbb{N} $.
Then,
given
any
subset
S $\subseteq$ E,
we
define
its
SE-tree
view:
Definition 2.1 A Node's View
$View(ind,S) \stackrel{def}{=} \{e \in E | ind(e) \gt max_{e' \in S} ind(e')\}$

In the paper there is an example of a tree made with what appears to be E={1,2,3,4}.  I have some familiarity with set-builder notation, but much of the other parts of the &quot;node's view&quot; is confusing me. I skimmed ahead to see if there were clarifications, but I didn't manage to find them so either: a) the author is assuming a competency I do not have, b) the explanation is there and I couldn't find it, or c) the author is doing a horrible job as an author.
So with the hope that it is one of the first two:

I'm assuming that the prime in e' is for the complement of the set e, so if e = {1}, then e' = {2,3,4}.  Is this correct?

What is this ind function?  What would ind({3,4}) be for example?

$max_{e' \in S}$?  Is this the maximum height of the sub tree of the complement of e?
Any assistance on this would be most appreciated.
Please, one question per question.

The answer to your first question: No, prime most likely does not indicate complement, absent some specific indication of that.  It is just another variable.  $e$ is one variable; $e'$ is another variable (the author could have used a different letter, like $f$ or $x$ or something, but chose to use $e'$ instead).

The answer to your second question: The ind function is defined in the text immediately preceding the definition.  Read it again?

Yes, it's possible you might lack the necessary mathematical background.  You might try taking an online course (or working through a textbook) on discrete mathematics for computer science.