Calculus of linear extensions and Newton interpolation. (arXiv:0911.5620v1 [math.CO])

We use Newton divided differences for calculation of Greene sums -- the
rational functions determined by linear extensions of partially ordered sets.
Identities for Greene sums generate relations for Newton divided differences
and Arnold differential forms. Also generalizations of the Newton interpolation
series which are indexed by sequences of partially ordered sets are received.

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Original source : http://arxiv.org/abs/0911.5620...