2000/11/28 by Manoj K. Chari, Chari, Manoj K., Michael Joswig +1
Computer Science · Mathematics · #05C50 #05C70) #05E25 (05A15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.CO #msc:05C50 #msc:05E25
paper · pdf · doi:10.48550/arxiv.math/0011234
12 pages, 3 figures
arxiv created 2000/11/28 · openalex publication_date 2000/11/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate properties of the set of discrete Morse functions on a simplicial complex as defined by Forman. It is not difficult to see that the pairings of discrete Morse functions of a finite simplicial complex again form a simplicial complex, the discrete Morse complex. It turns out that several known results from combinatorial topology and enumerative combinatorics, which previously seemed to be unrelated, can be re-interpreted in the setting of these discrete Morse complexes.