Counting Parity Palindrome Compositions

Counting Parity Palindrome Compositions is a study on compositions of positive integers that have the property of being both palindromic and having a parity structure. The authors, Andrews and Simay, present a simple formula for calculating the number of such compositions. They also provide a recursive proof for their theorem. The proof involves introducing new parts, adding to existing parts, and considering different types of compositions. The authors demonstrate the validity of their theorem for small values of n. They also verify that each composition is produced exactly once by categorizing them into different types. The study concludes by showing that the number of compositions triples at each stage and that one-third of the compositions belong to each type. This abstract summarizes the main findings of the study on counting parity palindrome compositions.