Raghavendra Tripathi

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20232026

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math.MG2025★ 2 cited

A note on Erdős matrices and Marcus\unicode{x2013}Ree inequality

Aman Kushwaha, Raghavendra Tripathi

In 1959, Marcus and Ree proved that any bistochastic matrix $A$ satisfies $Δ_{n} (A) := max_{σ \in S_{n}} \sum_{i = 1}^{n} A (i, σ (i)) - \sum_{i, j = 1}^{n} A (i, j)^{2} \geq 0$ . Erdős asked to charac…

math.MG2024

Some observations on Erdős matrices

Raghavendra Tripathi

In a seminal paper in 1959, Marcus and Ree proved that every $n \times n$ bistochastic matrix $A$ satisfies $∥ A ∥_{F}^{2} \leq max_{σ \in S_{n}} A_{i, σ (i)}$ where $S_{n}$ is…