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Nonfacets for shellable spheres

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Abstract

We generalize the notion of a map on a 2-sphere to maps on then-sphere and then show that there exist combinatorial types of countries that cannot be the only type of country for a shellablen-sphere. This generalizes the well known theorem that there are no maps on the 2-sphere all of whose countries arek-gons for anyk≧6.

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References

  1. D. Barnette,Generalized combinatorical cells and facet splitting, Pacific J. Math.57 (1975), 33–45.

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  2. H. Bruggesser and P. Mani,Shellable decompositions of cells and spheres, Math. Scand.29 (1971), 197–205.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 95616, Davis, Calif., USA

    D. Barnette

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  1. D. Barnette
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Research supported by N.S.F. grant, number GP-42941

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Barnette, D. Nonfacets for shellable spheres. Israel J. Math. 35, 286–288 (1980). https://doi.org/10.1007/BF02760653

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  • DOI: https://doi.org/10.1007/BF02760653

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