Enumeration of Deutsch paths by adding the adding-a-new-slice method and applications
Helmut Prodinger

TL;DR
This paper introduces a novel enumeration method for a variation of Deutsch paths, utilizing the adding-a-new-slice technique and kernel method to count specific path features and subclasses, extending combinatorial enumeration techniques.
Contribution
It develops the adding-a-new-slice method for enumerating Deutsch paths with arbitrary down-step lengths and applies it to count maximal runs and specialized subclasses.
Findings
Derived formulas for counting Deutsch paths with arbitrary down-steps.
Extended enumeration techniques to path subclasses satisfying Stanley's conditions.
Demonstrated the effectiveness of the adding-a-new-slice method in path enumeration.
Abstract
A variation of Dyck paths allows for down-steps of arbitrary length, not just one. This is motivated by ideas due to Emeric Deutsch. We use the adding-a-new-slice technique and the kernel method to compute the number of maximal runs of up-step runs of length 1 and a subclass of Deutsch paths satisfying a condition that was stipulated by R. Stanley for Dyck paths.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algorithms and Data Compression · semigroups and automata theory
