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All DE scales in this extended sense are also [[billiard scales]].<ref>Sano, S., Miyoshi, N., & Kataoka, R. (2004). m-Balanced words: A generalization of balanced words. Theoretical computer science, 314(1-2), 97-120.</ref>
All DE scales in this extended sense are also [[billiard scales]].<ref>Sano, S., Miyoshi, N., & Kataoka, R. (2004). m-Balanced words: A generalization of balanced words. Theoretical computer science, 314(1-2), 97-120.</ref>
== List of distributionally even circular words ==
Below is the complete list of distributionally even circular words up to 10 letters.
=== 1 Letter ===
1 letter, MV1: 0
=== 2 Letters ===
2 letters, MV1: 00
2 letters, MV2: 01
=== 3 Letters ===
3 letters, MV1: 000
3 letters, MV2: 001
3 letters, MV3: 012
=== 4 Letters ===
4 letters, MV1: 0000
4 letters, MV2: 0001, 0101
4 letters, MV3: 0102
4 letters, MV4: 0123
=== 5 Letters ===
5 letters, MV1: 00000
5 letters, MV2: 00001, 00101
5 letters, MV3: 00102, 01012
5 letters, MV4: 01023
5 letters, MV5: 01234
=== 6 Letters ===
6 letters, MV1: 000000
6 letters, MV2: 000001, 001001, 010101
6 letters, MV3: 001002, 012012
6 letters, MV4: 010203, 012013
6 letters, MV5: 012034
6 letters, MV6: 012345
=== 7 Letters ===
7 letters, MV1: 0000000
7 letters, MV2: 0000001, 0001001, 0010101
7 letters, MV3: 0001002, 0010201, 0101012, 0102012
7 letters, MV4: 0010203, 0102013, 0102032, 0120123
7 letters, MV5: 0102034, 0120134, 0120314
7 letters, MV6: 0120345
7 letters, MV7: 0123456
=== 8 Letters ===
8 letters, MV1: 00000000
8 letters, MV2: 00000001, 00010001, 00100101, 01010101
8 letters, MV3: 00010002, 01020102, 01021012
8 letters, MV4: 00100203, 01012013, 01020103, 01021013, 01230123
8 letters, MV5: 01020304, 01023042, 01230124
8 letters, MV6: 01023045, 01230145, 01230425
8 letters, MV7: 01230456
8 letters, MV8: 01234567
=== 9 Letters ===
9 letters, MV1: 000000000
9 letters, MV2: 000000001, 000010001, 001001001, 001010101
9 letters, MV3: 000010002, 001020102, 010101012, 012012012
9 letters, MV4: 001002003, 001020103, 001020302, 010201023, 010201032, 012031023
9 letters, MV5: 001020304, 010201034, 010201304, 010203042, 012013014, 012031024, 012301234
9 letters, MV6: 010203045, 012031045, 012301245, 012301425, 012301435, 012304135
9 letters, MV7: 012034056, 012301456, 012304156, 012304256
9 letters, MV8: 012304567
9 letters, MV9: 012345678
=== 10 Letters ===
10 letters, MV1: 0000000000
10 letters, MV2: 0000000001, 0000100001, 0001001001, 0010100101, 0101010101
10 letters, MV3: 0000100002, 0010200102, 0101201012, 0102102012
10 letters, MV4: 0001002003, 0010200103, 0010200302, 0101201013, 0102301023, 0120120123, 0120310213
10 letters, MV5: 0010200304, 0102103014, 0102301024, 0102301043, 0102304023, 0120130214, 0120310214, 0120310413, 0123401234
10 letters, MV6: 0102030405, 0102301045, 0102304025, 0102304053, 0120130145, 0120130415, 0120310415, 0120340253, 0123401235
10 letters, MV7: 0102304056, 0120340256, 0120340563, 0123401256, 0123401536
10 letters, MV8: 0120340567, 0123401567, 0123405267
10 letters, MV9: 0123405678
10 letters, MV10: 0123456789


== Related topics ==
== Related topics ==
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