defintion_of_subsets
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| defintion_of_subsets [2024/06/01 08:14] – [Complement of a magic series] mino | defintion_of_subsets [2024/09/07 11:58] (current) – external edit 127.0.0.1 | ||
|---|---|---|---|
| Line 16: | Line 16: | ||
| * We can define order on sets of distinct integers in accord with the order of their binary representation. | * We can define order on sets of distinct integers in accord with the order of their binary representation. | ||
| * Example: | * Example: | ||
| - | * A magic set { 5, 16, 2, 11 } is greater than { 12, 1, 15, 6 } because their binary representations are 1000 0100 0001 0010 ( = 0x8412 ) and 0100 1000 0010 0001 ( = 0x4821 ), respectively, | + | * A magic series |
| ==== Complement of a magic series ==== | ==== Complement of a magic series ==== | ||
| Line 32: | Line 32: | ||
| ==== The representative magic series of a magic square ==== | ==== The representative magic series of a magic square ==== | ||
| - | Every row and column of a magic square is always a magic series. We define the ** representative magic series ** of a magic square as **the largest magic series which forms a row, a column, the compliment | + | Every row and column of a magic square is always a magic series. We define the ** representative magic series ** of a magic square as **the largest magic series which forms a row, a column, the complement |
| Example: | Example: | ||
| Line 42: | Line 42: | ||
| | | ||
| - | is { 16, 13, 3, 2 } = 0x9006, which forms the compliment | + | is { 16, 13, 3, 2 } = 0x9006, which forms the complement |
| - | **We classify magic squares by their representative magic series. This classification is invariant under rotations, reflections, | + | **We classify magic squares by their representative magic series. This classification is invariant under rotations, reflections, |
| ** | ** | ||
defintion_of_subsets.1717197243.txt.gz · Last modified: 2024/06/01 08:14 by mino