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August 8, 2025Communications in Algebra

A representation-theoretic computation of the rank of 1-intersection incidence matrices: 2-subsets vs. n -subsets.

Joshua E. Ducey Colby J. Sherwood

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Key Points

The matrix rank is computed using representation theory, focusing on 1-intersection incidence matrices.
The primary result involves conditions for large p-rank in the matrix Wk,ni(m).
We consider both k-subsets and n-subsets of an m-element set during our analysis.
Understanding these ranks can lead to insights in combinatorics and algebraic structures.

Implication

Computation reveals the rank of incidence matrices for k-subsets and n-subsets, indicating special conditions for p-rank.

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Cite This Study

Ducey et al. (2025) studied this question.

synapsesocial.com/papers/68a365740a429f797332bda8 https://doi.org/10.1080/00927872.2025.2539431

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Keep reading

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1The rank distribution of matrices representing graphs with a long induced path over the field of two elements2025
2A Functorial Version of Chevalley's Theorem on Constructible Sets2024
3Sharp Rank Transitions and Supercritical Kernel Structure in Sparse Cayley Incidence MatricesOriginal Research · 2026
4Affine subspaces of matrices with rank in a range2024
5On affine spaces of rectangular matrices with constant rank2024

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