Fraenkel word: Difference between revisions

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# If {{!}}''w''{{!}} ≡ 0 mod 2''i''+1, then {{!}}''w''{{!}}'''i''' = {{!}}''w''{{!}}/2''i''+1.

# If {{!}}''w''{{!}} ≢ 0 mod 2''i''+1, then {{!}}''w''{{!}}'''i''' = either floor({{!}}''w''{{!}}/2''i''+1) or ceil({{!}}''w''{{!}}/2''i''+1).

#* More precisely, if for a given ''i'' we have ''w'' = ''uv'' or ''vu'' where ''u'' is a possibly empty word whose length is 0 mod 2''i''+1, and ''v'' ~~intersects~~ the middle of an ''F''''i''+1, then {{!}}''w''{{!}}'''i''' = ceil({{!}}''w''{{!}}/2''i''+1). Otherwise, {{!}}''w''{{!}}'''i''' = floor({{!}}''w''{{!}}/2''i''+1).

#* More precisely, if for a given ''i'' we have ''w'' = ''uv'' or ''vu'' where ''u'' is a possibly empty word whose length is 0 mod 2''i''+1, and ''v'' is a nonempty word intersecting the middle of an ''F''''i''+1, then {{!}}''w''{{!}}'''i''' = ceil({{!}}''w''{{!}}/2''i''+1). Otherwise, {{!}}''w''{{!}}'''i''' = floor({{!}}''w''{{!}}/2''i''+1).

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 # If {{!}}''w''{{!}} ≡ 0 mod 2<sup>''i''+1</sup>, then {{!}}''w''{{!}}<sub>'''i'''</sub> = {{!}}''w''{{!}}/2<sup>''i''+1</sup>.
 # If {{!}}''w''{{!}} ≢ 0 mod 2<sup>''i''+1</sup>, then {{!}}''w''{{!}}<sub>'''i'''</sub> = either floor({{!}}''w''{{!}}/2<sup>''i''+1</sup>) or ceil({{!}}''w''{{!}}/2<sup>''i''+1</sup>).
-#* More precisely, if for a given ''i'' we have ''w'' = ''uv'' or ''vu'' where ''u'' is a possibly empty word whose length is 0 mod 2<sup>''i''+1</sup>, and ''v'' intersects the middle of an ''F''<sub>''i''+1</sub>, then {{!}}''w''{{!}}<sub>'''i'''</sub> = ceil({{!}}''w''{{!}}/2<sup>''i''+1</sup>). Otherwise, {{!}}''w''{{!}}<sub>'''i'''</sub> = floor({{!}}''w''{{!}}/2<sup>''i''+1</sup>).
+#* More precisely, if for a given ''i'' we have ''w'' = ''uv'' or ''vu'' where ''u'' is a possibly empty word whose length is 0 mod 2<sup>''i''+1</sup>, and ''v'' is a nonempty word intersecting the middle of an ''F''<sub>''i''+1</sub>, then {{!}}''w''{{!}}<sub>'''i'''</sub> = ceil({{!}}''w''{{!}}/2<sup>''i''+1</sup>). Otherwise, {{!}}''w''{{!}}<sub>'''i'''</sub> = floor({{!}}''w''{{!}}/2<sup>''i''+1</sup>).
 }}