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Nov 15, 2021 at 16:31 comment added Sam Hopkins A general comment about the series of questions you have asked: there are some facts which follow from general theory of P-partitions as developed by Stanley and which apply to all posets; then there are some facts which are "two-dimensional" in nature and have to do with nonintersecting lattice paths, determinants, etc. and which apply only to special families of posets. Combining the two categories of facts (in the ways you have done) does lead to interesting conclusions...
Nov 15, 2021 at 16:28 comment added Sam Hopkins Is this not just what you get from the standard way of representing plane partitions as non-intersecting lattice paths and applying Lindstrom-Gessel-Viennot?
Nov 15, 2021 at 16:14 history asked Johann Cigler CC BY-SA 4.0