# Down-step statistics in generalized Dyck paths

@article{Asinowski2020DownstepSI, title={Down-step statistics in generalized Dyck paths}, author={Andrei Asinowski and Benjamin Hackl and Sarah J. Selkirk}, journal={Discret. Math. Theor. Comput. Sci.}, year={2020}, volume={24} }

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…

## 3 Citations

### Raised $k$-Dyck paths

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- 2022

Raised k -Dyck paths are a generalization of k -Dyck paths that may both begin and end at a nonzero height. In this paper, we develop closed formulas for the number of raised k -Dyck paths from (0 ,…

### Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo $k$

- Mathematics
- 2022

For fixed non-negative integers $k$, $t$, and $n$, with $t < k$, a $k_t$-Dyck path of length $(k+1)n$ is a lattice path that starts at $(0, 0)$, ends at $((k+1)n, 0)$, stays weakly above the line $y…

### MIN-turns and MAX-turns in k-Dyck paths: a pure generating function approach

- Computer Science
- 2021

k-Dyck paths differ from ordinary Dyck paths by using an up-step of length k. We analyze at which level the path is after the s-th up-step and before the (s + 1)st up-step. In honour of Rainer Kemp…

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