bogart so far, so far

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
(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).
* [ (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.


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

    cut-and-pasted from wilf.

  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 ]).

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