two necklaces interacting
Wouter Meeussen
w.meeussen.vdmcc at vandemoortele.be
Wed Aug 12 17:00:58 CEST 1998
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.
NV Vandemoortele Coordination Center
Oils & Fats Applied Research
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