2025/10/05 by Yu-Chuan Yu, Yu, Yu-Chuan, Chi Ho Yuen +1
Computer Science · Mathematics · #05B35 (Primary) #13F65 (Secondary) #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2510.04163
openalex publication_date 2025/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
White's conjecture asserts that any two tuples of matroid bases that have the same multi-set union can be transformed from one to another by symmetric exchanges; it also implies that the toric ideals of matroids are generated by the binomials encoding these exchanges. We prove White's conjecture for the class of paving matroids. Our strategy is to generalize the inductive argument using circuit-hyperplane relaxations in the recent work of Han et al. to stressed hyperplane relaxations.