Enumerations of humps and peaks in $(k,a)$-paths and $(n,m)$-Dyck paths via bijective proofs

Rosena R. X. Du, Yingying Nie, Xuezhi Sun

Recently Mansour and Shattuck studied $(k,a)$-paths and gave formulas that relate the total number of humps (peaks) in all $(k,a)$-paths to the number of super $(k,a)$-paths. These…