Mathematics of MOS: Difference between revisions

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# Binary and [[distributionally even]]

# Binary and balanced (for any ''k'', any two ''k''-steps ''u'' and ''v'' differ by either 0 or {{nowrap|L − s {{=}} c}})

# Mode of a Christoffel word. (If gcd(''p'',~~ ~~''q'') = 1, a ''Christoffel word with rational slope'' ''p''/''q'' is the unique path from (0, 0) and (''p'', ''q'') in the 2-dimensional integer lattice graph above the ''x''-axis and below the line {{nowrap|''y'' {{=}} (''p''/''q'')''x''}} that stays as close to the line as possible without crossing it.)

# Mode of a Christoffel word. (If {{nowrap|gcd(''p'', ''q'') {{=}} 1}}, a ''Christoffel word with rational slope'' ''p''/''q'' is the unique path from (0, 0) and (''p'', ''q'') in the 2-dimensional integer lattice graph above the ''x''-axis and below the line {{nowrap|''y'' {{=}} (''p''/''q'')''x''}} that stays as close to the line as possible without crossing it.)

While each characterization has a generalization to scale structures with more step sizes, the generalizations are no longer equivalent:

# [[Maximum variety]] n

# [[Maximum variety]] ''n''

# [[Generator-offset property]], [[generator sequence]]

# [[Distributional evenness]]

@@ Line 21: / Line 21: @@
 # Binary and [[distributionally even]]
 # Binary and balanced (for any ''k'', any two ''k''-steps ''u'' and ''v'' differ by either 0 or {{nowrap|L − s {{=}} c}})
-# Mode of a Christoffel word. (If gcd(''p'',&nbsp;''q'') = 1, a ''Christoffel word with rational slope'' ''p''/''q'' is the unique path from (0,&nbsp;0) and (''p'',&nbsp;''q'') in the 2-dimensional integer lattice graph above the ''x''-axis and below the line {{nowrap|''y'' {{=}} (''p''/''q'')''x''}} that stays as close to the line as possible without crossing it.)
+# Mode of a Christoffel word. (If {{nowrap|gcd(''p'', ''q'') {{=}} 1}}, a ''Christoffel word with rational slope'' ''p''/''q'' is the unique path from (0,&nbsp;0) and (''p'',&nbsp;''q'') in the 2-dimensional integer lattice graph above the ''x''-axis and below the line {{nowrap|''y'' {{=}} (''p''/''q'')''x''}} that stays as close to the line as possible without crossing it.)
 While each characterization has a generalization to scale structures with more step sizes, the generalizations are no longer equivalent:
-# [[Maximum variety]] n
+# [[Maximum variety]] ''n''
 # [[Generator-offset property]], [[generator sequence]]
 # [[Distributional evenness]]