AI 中文总结
本文证明欧拉三角是3阶全正的，对Brenti猜想给出部分肯定回答，并为几类广义欧拉三角建立了3阶全正性。
AI 中文摘要
Brenti猜想欧拉三角是全正的，本文证明欧拉三角是3阶全正的，从而对Brenti猜想给出部分肯定回答，此外还为几类广义欧拉三角建立了3阶全正性。
英文摘要
Brenti conjectured that the Eulerian triangle is totally positive. In this paper, we prove that the Eulerian triangle is totally positive of order 3, thereby providing a partial affirmative answer to Brenti's conjecture. In addition, we establish total positivity of order 3 for several families of generalized Eulerian triangles.
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