A symmetric variation of a distribution of Kreweras and Poupard

Abstract The distribution of Kreweras and Poupard refines the Narayana number by counting three different cases of lattice bridges, or Catalan sequences, with respect to four parameters. Here, a cycle lemma is established to derive a symmetric distribution that counts one variant of these cases. Variants of the other cases are then counted bijectively. Two bijections between a set of pairs of non-intersecting lattice paths are considered and related to the distribution.