Hook length formula and geometric combinatorics.

By Igor Pak. 2001

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Partition bijections, a survey (2006, background): “For Stanley’s formula, extension 9.1.5, other generalizations, a connection to symmetric functions and references, see [115], Chapter 7. The first bijective proof of MacMahon’s Theorem is found in [36]. Our presentation follows [ 107 ].”
Existence of unimodular triangulations — positive results (2014, background): “Other well known enumerative results involving unimodular triangulations include the proof of the hook-length formula by Pak [90] and Stanley’s observation that Eulerian numbers are volumes of hypersimplices [108] (see also Section 3.”
Plane partitions in the work of Richard Stanley and his school (2015, background): “of classical groups (as Richard Stanley pointed out; see Sections 4 and 7), representation theory of quantum groups (cf. [64]), enumeration of integer points in polytopes and commutative algebra (cf. [12, 79, 17] and the references therein), enumeration of matchings in graphs (cf. [62, 66]), and to ”
The Surprising Mathematics of Longest Increasing Subsequences (2015, unknown): “4], [92], [96].”