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It is only occasionally that context makes the difference; this paper is an exception.
Combinatorics is an honest subject ... You count balls in a box, and you either have the right number or you haven’t. .
The subject of this paper is certain new combinatorial inequalities for hook numbers of Young diagrams, rooted trees, and their generalizations. In two special cases, these inequalities are known, have technical...
We are grateful to Joshua Swanson for telling us about Swanson (2018) and for his careful reading of the manuscript. The first author is thankful to Alejandro Morales and Greta Panova for numerous interesting conversations about the Naruse hook-length formula. We are also grateful to BIRS, in Banff, Canada, for hosting the first two authors at the Asymptotic Algebraic Combinatorics workshop in March 2019, where this paper was finalized. This collaboration began when the first author asked a question on MathOverflow. (See http://mathoverflow.net/q/243846). The first author was partially supported by the NSF. The second and third authors were partially supported by the RSCF (Grant 17-71-20153).
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