Dictionary Order & Alphabet
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Letter positions and shifts
Position from the right
p_{\text{right}} = 27 - p_{\text{left}}
The two positions of the same letter add to 27.
Shifted position
p' = p \pm k
Move right (+) or left (−) by k letters, staying inside 1 to 26.
Dictionary rank and word surgery
Rank of a word
\text{rank} = 1 + \sum_i c_i \times (r_i)!
c_i = unused letters smaller than the letter at position i; r_i = letters remaining after position i.