Year: 2015
Type: preprint
Abstract: Polytope numbers for a given polytope are an integer sequence defined by the combinatorics of the polytope. Recent work by H. K. Kim and J. Y. Lee has focused on writing polytope number sequences as sums of simplex number sequences. We focus on $r$-rectified simplices and show that the sequences for these polytopes can be written as alternating sums of simplex numbers analogous to the inclusion-exclusion given by the geometric process of $r$-rectification.
Source: arXiv (Cornell University)
Authors: Jackson, Michael A., Smith, Doug, Jantsch, Peter, Scurlock, Christina, Snyder, Chelsea, Fairchild, Eric, Mabe, Robin, Polaski, Emma
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W832392341