Annals of Combinatorics 1 (1997) 353-366


Kinematic Formulas for Finite Lattices

Daniel A. Klain

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
klain@math.gatech.edu

Received November 10, 1997

AMS Subject Classification: 05A05; 05A10, 05A19, 05A25, 52A22

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.

Keywords: kinematic formula, invariant, valuation, lattice


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