What does this research mean for the field?

A connected skew diagram is uniquely determined up to translation by two boundary observations, such as its skew Schur function combined with that of its first-row deletion or a northeast row extension of any positive length. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To determine whether connected skew diagrams can be reconstructed up to translation from boundary observations and to examine the rigidity of their cofactor coordinates.

September 14, 2026Open Access

Boundary reconstruction and cofactor rigidity for skew Schur functions

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Authors

JSJohn Shields

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Implication

Mathematical analysis demonstrates boundary reconstruction of connected skew diagrams up to translation, indicating algebraic rigidity in skew Schur functions.

Key Points

To determine whether connected skew diagrams can be reconstructed up to translation from boundary observations and to examine the rigidity of their cofactor coordinates.
Analyzed strictly Monge properties of the Jacobi–Trudi staircase induced by strict convexity.
Applied successive prefix minor elimination and leading monomial quotients to reconstruct row and column parameters sequentially.
Evaluated cofactor differences for skew diagrams sharing a common inner boundary across admissible strictly convex weights.
A connected skew diagram is uniquely determined up to translation by its skew Schur function paired with either its first-row deletion or a northeast row extension of any positive length.
Reconstruction also succeeds from two extensions of distinct positive lengths without providing the lengths or the original diagram's function.
Cofactor differences display a rigid adjacent-edge fingerprint with single-monomial initial forms matching the local adjacency structure of McNamara–van Willigenburg compositions.

Cite This Study

John Shields (2026) studied this question.

synapsesocial.com/papers/6aa7b3aa0926e14a848b2d78 https://doi.org/10.5281/zenodo.22723463

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Implication

Mathematical analysis demonstrates boundary reconstruction of connected skew diagrams up to translation, indicating algebraic rigidity in skew Schur functions.

Boundary reconstruction and cofactor rigidity for skew Schur functions

Discussion

Member takes

Implication

Key Points

Cite This Study

Boundary reconstruction and cofactor rigidity for skew Schur functions

Discussion

Member takes

Implication

Key Points

Cite This Study

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