Section II: Structures

Inversion, while a key component of the apparatus necessary for understanding the dynamics of Palindromes, is not the only linguistic operation involved in the formation of Palindromes. The pure involutive property of Palindromes (e.g., \(\zeta = {\zeta}^{-1})\) only manifests in a rare class of Sentences known as Perfect Palindromes, to be defined shortly.

However, the vast majority of Palindromes in any language are not pure involutions. Instead, the operation of inversion usually degrades the semantic content of a Sentence by re-ordering the Delimiters, as seen in the following,

\[\zeta = \text{now sir a war is won}\]

\[{\zeta}^{-1} = \text{now si raw a ris won}\]

In order to properly understand the nature of a Palindrome, the system requires a method of quantifying the distribution of Delimiters in a Sentence and making claims about the structure of that distribution. Furthermore, it must have a method of removing the “impurities” in Delimiter distributions that are introduced through inversion.

Contents:

• Section II.I: Delimiter Count
  • Definition & Examples
  • Properties
  • Theorems
• Section II.II: Pivots
  • Pivot Characters
  • Pivot Words
  • Subvertible Sentences
• Section II.III: Reductions
  • Definition & Examples
  • Properties
  • Theorems
• Section II.IV: Palindromes
  • Definition & Examples
  • Aspect
  • Parity
• Section II.V: Summary