TL;DR
This paper extends the study of modular palindromic and anti-palindromic compositions by introducing partial symmetry measures, deriving formulas, and uncovering new connections with known integer sequences.
Contribution
It generalizes previous work by considering all compositions partially palindromic or anti-palindromic, providing formulas and bijective proofs, and linking to OEIS sequences.
Findings
Derived closed-form formulas for partial palindromic compositions.
Established bijective proofs for enumeration results.
Connected new composition classes to known OEIS sequences.
Abstract
We generalize recent work of Andrews, Just, and Simay on modular palindromic compositions and anti-palindromic compositions by viewing all compositions partially (modular) palindromic or anti-palindromic. More precisely, we enumerate compositions by the extent to which they are (modular) palindromic or anti-palindromic. We obtain various closed formulas from generating functions and provide bijective proofs for many of them. We recover some known results of Andrews, Just, and Simay and discover new connections with numerous sequences in The On-Line Encyclopedia of Integer Sequences (OEIS).
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · semigroups and automata theory · Polynomial and algebraic computation