MAR 3 1 1965

Cropé Divn.
Ft. Detrick, Md. 21701
165 March 30

Memo to Notationers:

Dr. Joshua Lederberg has called my attention to the fact that we
seem to be dealing with "Hamiltonian Circuits" in our locant paths. We
might see some additional clarifications by a fairly exhaustive (is it?)
checkout of all possible locant paths, forward and backward, in the very
elementary form of a trigonal prism, made asymmetric by the addition of
one point on a parallel edge, and a second point on an opposing side.

Thirty locant paths are drawn on the attached diagram. Those that
are "counted" in three rings (in completing order of rings!) are circled
and underlined in the "dictionary definitions" of loop-forming pairs.

Each "Hamiltonian cireuit" (if that is the proper name) can be
analyzed completely from JUST ONE DIAGRAM, CHOSEN TO EMPHASIZE SYMMETRY
AND THEREBY AVOID UNNECESSARY DUPLICATION OF TRIALS. I do it thus:
can shift 7 tines when

 

Path #1: LINK RING NOTATION h ach Vink is present,
ae abede a5 g b (Pattern
af aef a3 f c check)

gc abcef ad e a
bh begh bh

Check: a3 b3 ¢3 deo fo gp h = 17 (sum of ring numbers )
~~ azkakak&b=5 (locant sum)

 

I feel very strongly that our task is to analyze the circuits, not draw
various kinds of diagrams. I like to draw, but computers cannot sketch
this abstract topological information exactly as we do.

Hoping this stimulates some progress at Detroit!

Hastily,

br
30 "HAMILTONIAN CIRCUIT“! TN §-rO2NTED TRIANGULAR PRISM
Nonconsecutive links identify eac: 3
(Alphabetic order is reversed if cited

  

vterh. Tocant sum is shown in Lower right.
Locan*, is not the lowest in formed ring.)
+ 5 Gu=ure

“G

CAS oet

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Jpamtwer ieee

  

5 7 6

be ag ah hd| ae af gc hd
}9 {1 c

ae af gc bh
-F

 

=

   
  
   
   
       

nnn ne
{ ?
A
v
’
»

ame ewe eee an

‘
é

      

ae cf ah hd
\3=n5

ae af ah he
17

 

 

af

|

ean ew

    

Asem

 

ac dg bf ah | «-
24

 

%
.
.
~

ee
Aenea ee
aoe fee

D
w

ae df gb he | ae df bg ah
26 ~3 (27 <= -10

-A
Ne

   

 

   

ae

——wf..

  

 

 

 

 

 

 

 

 

be ag he fh | ad cg ah fh | ‘bd cg ah en, be ge ah fh

ad ag he fh ; of eg ah he

 

165 MAR 30/ wow