Introduction to Tropical Combinatorics

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Macdonald processes (2011, background): “Kirillov’s [62, 76] tropical RSK correspondence, Corwin, O’Connell, Seppäläinen and Zygouras [32] introduce a different Whittaker process to describe the free energy hierarchy for this polymer (see Section 5.”
An Invitation to the Generalized Saturation Conjecture (2004, background): “, see [38], [36], and a fermionic formula for the parabolic Kostka polynomials Kλ,R(q) corresponding to a dominant sequence of rectangular shape partitions R, see e.”
Tropical Combinatorics and Whittaker functions (2011, methodology): “Geometric RSK correspondence In this section we describe an extension of Kirillov’s ‘tropical’ (or presently ‘geometric’) RSK correspondence [36] to rectangular matrices.”
Directed polymers and the quantum Toda lattice (2009, background): “The mapping η[0,t] → ({( kη)i(t),1 ≤ i ≤ k ≤ N}, {T η(s), s ≤ t}) is a continuous version of the geometric (or “tropical”) RSK introduced by Kirillov [34] (see also [4, 39]).”
Discrete Dynamical Systems with W(A(1)m−1 × A(1)n−1) Symmetry (2002, background): “Since the Weyl group actions are tropical [2] (i.”
The Kardar-Parisi-Zhang equation and universality class (2011, background): “The first is the existence of a finite temperature version of RSK — the tropical RSK correspondence introduced by Kirillov [101] in the context of tropical combinatorics.”