two necklaces interacting

[Wouter Meeussen]

hi,

two facing necklaces, one above the other, each n positive and n negative
charges. Count the number of inter-necklace energy levels. Total number of
configurations is (2n choose n)^2 : Outer product of perms x perms. The
diagonal of this matrix corresponds to the levels of a single necklace.

n	lev	({level_count,degeneracy},...)

2	2	{{2,2}}

4	5	{{2,2},{2,4},{1,24}}

6	18	{{2,2},{2,6},{4,12},{4,24},{4,36},{2,48}}

8	71	{{2,2},{2,4},{4,8},{14,16},{12,32},{4,48},{18,64},{2,96},
		{8,128},{2,160},{2,320},{1,728}}

10	538	{{2,2},{6,10},{34,20},{92,40},{8,60},{268,80},{2,100},
		{4,120},{56,160},{4,240},{16,280},{16,320},{4,380},{2,400},
		{2,440},{12,480},{4,640},{4,720},{2,1280}}


wouter.

ps. when comparing these results to more classical combinatorics, beware of
the "accidental degeneracies" that can be present here too.



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