  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).
