Down-step statistics in generalized Dyck paths

  title={Down-step statistics in generalized Dyck paths},
  author={Andrei Asinowski and Benjamin Hackl and Sarah J. Selkirk},
  journal={Discret. Math. Theor. Comput. Sci.},
The number of down-steps between pairs of up-steps in $k_t$-Dyck paths, a generalization of Dyck paths consisting of steps $\{(1, k), (1, -1)\}$ such that the path stays (weakly) above the line $y=-t$, is studied. Results are proved bijectively and by means of generating functions, and lead to several interesting identities as well as links to other combinatorial structures. In particular, there is a connection between $k_t$-Dyck paths and perforation patterns for punctured convolutional codes… 

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