Kostka semigroups and generalized Dyck paths
Jaehyung Kim
TL;DR
This paper proves a conjecture about the reducibility of generalized Dyck paths, providing a new proof and strengthening the Width Bound Theorem related to the Hilbert basis of the Kostka semigroup.
Contribution
It offers a new proof of the Width Bound Theorem and confirms the reducibility conjecture for generalized Dyck paths, advancing understanding of Kostka semigroups.
Findings
Confirmed reducibility of certain generalized Dyck paths
Provided a new proof for the Width Bound Theorem
Strengthened the theoretical framework of Kostka semigroups
Abstract
We prove a conjecture of S. Gao-J. Kiers-G. Orelowitz-A. Yong which asserts the reducibility of certain generalized Dyck paths. This gives a strengthening, and new proof, for their Width Bound Theorem on the Hilbert basis of the Kostka semigroup.
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Taxonomy
TopicsDigital Image Processing Techniques · Topological and Geometric Data Analysis · Mathematical Dynamics and Fractals