Graduation Year
2000
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Francis Su
Reader 2
Arthur Benjamin
Abstract
In this thesis, we provide constructive proofs of serveral generalizations of Sperner's Lemma, a combinatorial result which is equivalent to the Brouwer Fixed Point Theorem. This lemma makes a statement about the number of a certain type of simplices in the triangulation of a simplex with a special labeling. We prove generalizations for polytopes with simplicial facets, for arbitrary 3-polytopes, and for polygons. We introduce a labeled graph which we call a nerve graph to prove these results. We also suggest a possible non-constructive proof for a polytopal generalization.
Recommended Citation
Peterson, Elisha, "Combinatorial Proofs of Generalizations of Sperner's Lemma" (2000). HMC Senior Theses. 124.
https://scholarship.claremont.edu/hmc_theses/124
