### bogart so far, so far

or,
contents-page for
the “combinatorics” category of
_a_grader’s_notes_ (so far).
(in its natural order.)

a couple of good exercises
at random before breakfast
(april 17)
handwritten marginal translations:
english-to-code & code-to-english.

hey. this is fun and easy. (april 17)
the ross-collection copy of bogart
(1983) falls into my hands and i begin
to annotate it.

bogart so far (progress report at
random)
(april 21) longish.
stirling numbers of the second kind.
(i’ve got it this time at last.)
the “onto arrow” —–>> and its ilk.

a thing unto itself (april 25)
more about KPB2.3
(= bogart \section 2.3).
specifically,”
* [ (k)_n counts one-to-one F^n’s]
* [ k^n (counts functions)]
* [ S(n,k)k! counts “onto”
functions N_n —->> N_k]
“.
also… filling a much-needed gap…
N_k = {1, 2, … ,k}.
(why *is* there no standard symbol
for these amazingly-useful sets?)
${\Bbb N}_k := \{i\}_{i=1}^k$

bogart so far, so far (april 26)
this very post, in some weird
go-to-hell-escher-and-back self-
reference-gone-mad. (what’s next,
two spocks at once?)

and that’s it. heck, if it’d been
a *big* project, i’d’ve never taken
it on. BIJAGDH. maybe some day…
maybe today!… i’ll say something
about the infuriating treatment of
“the basic counting functions” or
the amazing “poyla’s change-making
example”. not now.

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#### 2 Comments

1. * Recall that [n] is the set {1,2,…,n}.

cut-and-pasted from wilf.
http://www.math.upenn.edu/~wilf/gfologyLinked2.pdf

2. [n] is also, alas, generic for
“the class of n”… and also
appears (alas twice… no,
wait. it’s complicated) *very*
often as the “greatest-integer”
function, better-known (in my
view) as the “floor” function:
$[x \mapsto \lfloor x \rfloor ]$).

• ## (Partial) Contents Page

Vlorbik On Math Ed ('07—'09)
(a good place to start!)