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A complete solution to the biased Alon-Krivelevich-Spencer-Szabó criterion problem for the discrepancy game Scaffolds for Higher Tropical Grassmannians: Foundations Krahn-Szegő type inequalities for graphs $\boldsymbol{2}$-Neighbor Bootstrap Percolation on Odd Graphs Modular inequalities and Alexander polynomials of pencil type conic-line arrangements Counterexamples regarding elementary symmetric partitions Bounds on Multiple $b$-Burst Deletion-Correcting Codes The mex statistic on combinatorial structures Proper Additive Edge Colorings of Regular Graphs Off-diagonal Ramsey numbers Finding Kissing Numbers with Game-theoretic Reinforcement Learning Directed Hamiltonicity in Generalized Kneser Graphs Inferring DAGs and Phylogenetic Networks from Least Common Ancestors Additive structures imply more distances in $\mathbb{F}_q^d$ Semi-inducibility of 4-vertex graphs A Structural Condition on Point Sets with Few Distinct Dot Products A quantum N-dimer model Möbius transforms and Shapley values for vector-valued functions on weighted directed acyclic multigraphs Well quasi-order and atomicity for combinatorial structures under consecutive orders The Permanent Rank of a Matrix (Part Three) Note on the Additive Basis Conjecture Complexity of the Zero Set of a Matrix Schubert Ideal The existence of unexpected automorphisms in direct product graphs Reconstruction of oriented matroids from Varchenko-Gelfand algebras Addition theorems for Ziegler pairs of hyperplane arrangements Combinatorial proofs of Petrie Pieri rule and Plethystic Pieri rule Asymptotic structure. 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Patterns that require distinct singular values
Caleb Cheung, Bryan Shader · 2025-11-16 · via math.CO updates on arXiv.org

Patterns of m by n matrices of term-rank m for which every real matrix with the pattern has no multiple singular value are characterized. This generalizes Fiedler's characterization of the paths being the only graphs for which every real symmetric matrix with the given graph has no repeated eigenvalue.

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