Mathematics of MOS: Difference between revisions

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# Binary and [[distributionally even]]
# 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}})
# 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. (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 without crossing it.)
# 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 without crossing it.)


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