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Kinematic formulas for finite lattices

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Abstract

In analogy to valuation characterizations and kinematic formulas of convex geometry, we develop a combinatorial theory of invariant valuations and kinematic formulas for finite lattices. Combinatorial kinematic formulas are shown to have application to some probabilistic questions, leading in turn to polynomial identities for Möbius functions and Whitney numbers.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332-0160, Atlanta, GA, USA

    Daniel A. Klain

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  1. Daniel A. Klain
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Research supported in part by NSF grant #DMS 9626688.

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Klain, D.A. Kinematic formulas for finite lattices. Annals of Combinatorics 1, 353–366 (1997). https://doi.org/10.1007/BF02558486

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  • DOI: https://doi.org/10.1007/BF02558486

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