arXiv subjects

Yinjie Li

Publications and source records attributed to Yinjie Li.

5 recordsLinked to original sources

arXiv2026

The Colomo-Pronko conjecture for frozen-corner alternating sign matrices

We prove the Colomo-Pronko conjecture for alternating sign matrices with a prescribed square of zeros at a corner, for all matrix sizes and freezing parameters. A known multiple-integral formula for the frozen-corner count yields determinant representations built from fixed polynomial kernels. We relate these kernels to the conjectured determinant through an inverse identity for the commutator of a signed Pascal matrix with reversal. In odd dimension, the comparison uses the one-dimensional nullspace and projection along it to eliminate the central coordinate. Combined with the asymptotic analysis of Colomo and Pronko, our result removes the conjectural assumption from their GUE Tracy-Widom fluctuation theorem for the intersection of the frozen boundary with the main diagonal in uniformly random alternating sign matrices. The finite-dimensional algebraic core of the proof has been formalized in Lean 4.

math.CO↗

arXiv2026

Lieb's Permanental Dominance Conjecture for Ordinary Immanants through Order Fifteen

Pate proved ordinary irreducible-immanant permanental dominance through order $13$ and identified $(4,4,3,3)$ as the sole remaining order-$14$ case, with $(5,4,3,3)$ and $(3^5)$ forming the order-$15$ frontier. These three cases are settled here; consequently $d_λ(A)/f^λ\le \operatorname{per}(A)$ for every partition $λ\vdash n$ with $n\le15$ and every complex Hermitian positive-semidefinite matrix $A$. The argument also yields results beyond this finite frontier: an exact four-term bridge for $(4,4,3,3)$, the uniform family $(m,4,3,3)$, a two-parameter family $(a,b,3,3)$ for $a\ge b\ge4$ and $5a\ge8b$, and a long-first-row criterion for arbitrary fixed tails. These results arise from explicit specializations of Pate's $W$-function positivity framework using partial swaps, Young projectors, Pieri--content identities, and branching data. For $(3^5)$, an exact Farkas certificate shows that the central-projector partial-swap cone is insufficient; a branching-refined one-swap construction escapes this obstruction and yields a positive $106+19$-witness certificate. Boundary-compression and node-moving results further describe the reach and limitations of the local-filter method. All finite certificates are checked by exact integer or rational arithmetic and are supplied as ancillary material. The order-$14$ bridge is additionally formalized and kernel-checked in Lean 4 for all complex Hermitian positive-semidefinite matrices, including the exact coefficient normalization and the deduction of $(4,4,3,3)$ permanental dominance from four explicitly stated Pate inequalities.

math.CO↗

arXiv2026

The S-matrix conjecture

Harwit and Sloane conjectured that every nonsingular entrywise-nonnegative matrix $A\in\mathbb R^{n\times n}$ satisfies $\|A^{-1}\|_F\ge 2n(n+1)^{-1}\|A\|_{\max}^{-1}$, with equality precisely for positive multiples of $S$-matrices. Cheng proved the conjecture in odd dimensions, while Frankel and Urschel proved the even-dimensional case for $n\ge1000$. We complete the remaining even-dimensional cases. Starting from the structural identities in Frankel--Urschel Lemma 2.1, we derive an exact global defect budget and combine binary rounding with Gram projection. A refined ten-row obstruction handles every even $n\ge66$; a finite exact calculation handles $4\le n\le64$, $n\ne6$; and a separate multi-column energy argument treats $n=6$. The order-two case follows from a direct calculation. The new even-dimensional proof has been formalized in Lean 4, with Frankel--Urschel Lemma 2.1 as its sole external mathematical input. Together with Cheng's odd-dimensional theorem, this proves the S-matrix conjecture in every dimension.

math.CO↗

arXiv2024

Detection and Utilization of Reflections in LiDAR Scans Through Plane Optimization and Plane SLAM

In LiDAR sensing, glass, mirrors and other material often cause inconsistent data readings, because the laser beams may report the distance of the glass, the distance of the object behind the glass or the distance to a reflected object. This causes problems in robotics and 3D reconstruction, especially with respect to localization, mapping and thus navigation. With dual-return LiDARs and other methods, one can detect the glass plane and classify the points in a single scan. In this work we go one step further and construct a global, optimized map of reflective planes, in order to then classify all LiDAR readings at the end. As our experiments will show, this approach provides superior classification accuracy compared to the single scan approach. The code and data for this work are available as open source online.

cs.RO↗

arXiv2023

The SLAM Hive Benchmarking Suite

Benchmarking Simultaneous Localization and Mapping (SLAM) algorithms is important to scientists and users of robotic systems alike. But through their many configuration options in hardware and software, SLAM systems feature a vast parameter space that scientists up to now were not able to explore. The proposed SLAM Hive Benchmarking Suite is able to analyze SLAM algorithms in 1000's of mapping runs, through its utilization of container technology and deployment in a cluster. This paper presents the architecture and open source implementation of SLAM Hive and compares it to existing efforts on SLAM evaluation. Furthermore, we highlight the function of SLAM Hive by exploring some open source algorithms on public datasets in terms of accuracy. We compare the algorithms against each other and evaluate how parameters effect not only accuracy but also CPU and memory usage. Through this we show that SLAM Hive can become an essential tool for proper comparisons and evaluations of SLAM algorithms and thus drive the scientific development in the research on SLAM.

cs.RO↗