2012/06/04 by H. K. Kim, J. Y. Lee, Kim, H. K. +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1206.0511
openalex publication_date 2012/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Polytope numbers for a polytope are a sequence of nonnegative integers that are defined by the facial information of a polytope. Every polygon is triangulable and a higher dimensional analogue of this fact states that every polytope is triangulable, namely, every polytope can be decomposed into simplexes. Thus it may be possible to represent polytope numbers by sums of simplex numbers. We analyzes a special type of triangulation, called pointed triangulation, and develops several methods to represent polytope numbers by sums of simplex numbers.