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Apr 16, 2016 at 12:11 comment added Per Alexandersson @ViditNanda: My main interest is showing positivity in different polynomial bases, say Schur positivity.
Apr 16, 2016 at 4:09 comment added darij grinberg I remember Viviane Pons telling me once that she found a bijection between two objects (in Catalan combinatorics) by narrowing down the search space by requiring the bijection to respect some statistics (after checking with Sage that said statistics were equidistributed). Sadly, I don't remember the details.
Apr 16, 2016 at 3:59 comment added Vidit Nanda This question, while interesting, is extremely broad in scope. An enormous family of examples comes just from the topological invariance of Euler characteristic! Are you simply looking for successful examples of categorification, or is there a more specific purpose to your question?
Apr 16, 2016 at 3:29 history asked Per Alexandersson CC BY-SA 3.0