SIAM Journal on Applied Algebra and Geometry· 2026Q1
Rank and Symmetries of Signature Tensors
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- Q1SCImago
- 2026year
Short summary
This paper establishes a sharp upper bound on the rank of signature tensors for piecewise linear paths and proves that skew-symmetric signature tensors of order three or more do not exist.
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Key points
- A sharp upper bound for the rank of signature tensors of piecewise linear paths is proven.
- Skew-symmetric signature tensors of order three or higher do not exist.
- Partial symmetries in signature tensors are shown to occur only for order three tensors.
- A geometric characterization is provided for paths with non-concise signature tensors.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract. The signature of a path is a sequence of tensors which allows for the unique reconstruction of a path. In this paper, we propose a systematic study of basic properties of signature tensors starting from their rank, symmetries, and conciseness. We prove a sharp upper bound on the rank of signature tensors of piecewise linear paths. We show that there are no skew-symmetric signature tensors of order three or more and prove that specific instances of partial symmetry can only happen for tensors of order three. Finally, we give a simple geometric characterization of paths whose signature tensors are not concise.
The authors' abstract, as published at the source. SIAM Journal on Applied Algebra and Geometry, 2026 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics