CyclicShiftIndex on BinaryWord
The position of the word among its distinct cyclic shifts in lexicographic order, from 0.
FindStat's St001436. The shifts are compared as binary numerals, which orders words of one length lexicographically; the table starts with a numeral above every shift's.
Called as CombinatorialStat(x, "CyclicShiftIndex"). The head's page has its examples.
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Distribution
Over BinaryWords at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001436
The index of a given binary word in the lex-order among all its cyclic shifts.
| Object | Value |
|---|---|
0 | 0 |
1 | 0 |
00 | 0 |
01 | 0 |
10 | 1 |
11 | 0 |
000 | 0 |
001 | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001436 has the rest.