Antipalindromic

English

Adjective

1. Template:Lb Being equivalent to the object whose constituents or parameters are reversed in order and mapped by some involution, particularly the inversion operator of a quasigroup.
   1. Of a polynomial, being equivalent to the polynomial with reversed and additively inverted coefficients: $\sum _{i=0}^n{a}_i{x}^i$ is antipalindromic iff $\sum _{i=0}^n{a}_i{x}^i=\sum _{i=0}^n-a_{n-i}{x}^i⟺a_i=-a_{n-i}$.

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   2. Of a natural number, with respect to base $b$, being equivalent to the natural number whose digits are reversed and subtracted from $b-1$: $\sum _{i=0}^n{a}_i{b}^i$ is antipalindromic iff $\sum _{i=0}^n{a}_i{b}^i=\sum _{i=0}^n(b-1-a_{n-i})b^i⟺a_i=b-1-a_{n-i}$.

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Related terms

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See also

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