Connectivity of Alternating Sign Triangle
Son Nguyen
TL;DR
This paper proves that the set of alternating sign triangles is connected, extending the known connectivity property from alternating sign matrices to this related combinatorial structure.
Contribution
It establishes the connectivity of alternating sign triangles, a property previously known for alternating sign matrices, thus advancing understanding of their combinatorial structure.
Findings
Proves the connectivity of alternating sign triangles
Extends properties known for alternating sign matrices
Provides new insights into cube recurrence relations
Abstract
Alternating sign triangles were introduced by Carroll and Speyer in relation to cube recurrence, by analogy to alternating sign matrices for octahedron recurrence. In this paper, we prove the connectivity of alternating sign triangles, which is analogous to the connectivity of alternating sign matrices.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Molecular spectroscopy and chirality · Mathematical Dynamics and Fractals