[seqfan] Sowing partitions of n
Eric Angelini
Eric.Angelini at kntv.be
Sun Dec 4 01:05:28 CET 2011
Hello SeqFans,
S = 2,1,2,3,3,7,6,4,10,5,6,9,7,13,9,8,13,15,10,17,13,11,16,12,16,20,15,14,22,21,17,25,21,20,27,18,22,19,28,29,30,31,25,22,28,27,29,24,30,35,31,26,...
A short explanation:
N = 1,2,3,4,5,6,7,8, 9 ,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,...
S = 2,1,2,3,3,7,6,4,10, 5, 6 ,9, 7,13, 9, 8,13,15,10,17,13,11,16,12,...
The natural 1 has moved 1 column right: discrepancy = 1 (from line N to line S)
2 has moved 1 column left + 1 column right: discrepancy = 1+1=2
3 has moved 1 column right + 2 columns right: discrepancy = 1+2=3
4 has moved 4 columns right: discrepancy = 4
5 has moved 5 columns right: discrepancy = 5
6 has moved 1 column right + 5 columns right: discrepancy = 1+5=6
7 has moved 1 column left + 6 columns right: discrepancy = 1+6=7
8 has moved 8 columns right: discrepancy = 8
9 has moved 3 columns right + 6 columns right: discrepancy = 3+6=9
10 has moved 1 column left + 9 columns right: discrepancy = 1+9=10
11 has moved 11 columns right : discrepancy = 11
12 has moved 12 columns right : discrepancy = 12
13 has moved 1 column right + 4 columns right + 8 columns right : discrepancy = 1+4+8=13
... etc.
Thus we kinda sow the partitions of n, starting to sow in the leftmost empty hole,
if possible, then sowing integers to the right, always trying to sow the smallest
integer of n's partition, then the second smallest, then the third, etc.
Best,
É.
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