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arXiv · 1507.01654

Rectified Simplex Polytope Numbers

Michael A. Jackson·Doug Smith·Peter Jantsch·Christina Scurlock·Chelsea Snyder·Eric Fairchild·Robin Mabe·Emma Polaski
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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.

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Michael A. Jackson, Doug Smith, Peter Jantsch, Christina Scurlock, Chelsea Snyder, Eric Fairchild, Robin Mabe, Emma Polaski. 2015-07-07. Rectified Simplex Polytope Numbers. https://arxiv.org/abs/1507.01654

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