2011/01/12 by Ardila, Federico, Owen, Megan, Sullivant, Seth · 1 citation
#Combinatorics (math.CO) #Computational Geometry (cs.CG) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1101.2428
We describe an algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex. A key tool is a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs. This correspondence also gives an explicit realization of such a complex as the state complex of a reconfigurable system, and a way to embed any interval in the integer lattice cubing of its dimension.