PreprintCC0arXiv
Eulerian triangle is totally positive of order 3
Abstract
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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BibTeX
@misc{mao2026eulerian,
title = {{Eulerian triangle is totally positive of order 3}},
author = {Jianxi Mao},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29224},
eprint = {2608.29224},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29224},
note = {CC0},
}
RIS
TY - UNPB
TI - Eulerian triangle is totally positive of order 3
AU - Jianxi Mao
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29224
UR - https://arxiv.org/abs/2608.29224
AB - 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.
ER -