Skew-symmetric Vanishing Lattices and Intersections of Schubert Cells

1998/02/19 by B. Shapiro, Boris Shapiro, Shapiro, B. +6 · 1 citation
Computer Science · Mathematics · #14M15 (Primary) 14N10 #14P25 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Topological and Geometric Data Analysis #math.AG #math.CO #msc:14M15 #msc:14N10 #msc:14P25

paper · pdf · doi:10.48550/arxiv.math/9802093

24 pages, 7 figures, AMSTeX, submitted to IMRN

arxiv created 1998/02/19 · openalex publication_date 1998/02/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the number of connected components in the intersection of two open opposite Schubert cells in the variety of complete real n-dimensional flags equals 3*2^n-1 for n>5.

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• Homotopy Type of Intersections of Real Bruhat Cells in Dimension 6

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