2013/05/24 by Fred B. Holt, Holt, Fred B. · 1 citation
Mathematics · #52B11 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #math.CO #msc:52B11
paper · pdf · doi:10.48550/arxiv.1305.5622
arxiv created 2013/05/24 · openalex publication_date 2013/05/24 · arxiv updated 2013/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Francisco Santos has described a new construction, per- turbing apart a non-simple face, to offer a counterexample to the Hirsch Conjecture. We offer two observations about this perturbed wedge con- struction, regarding its effect on edge-paths. First, that an all-but- simple spindle of dimension d and length d + 1 is a counterexample to the nonrevisiting conjecture. Second, that there are conditions under which the perturbed wedge construction does not increase the diameter. NOTE: These are simply working notes, offering two observations on the construction identified by Santos.