24 citations · 53 across the 11 of their papers we have counts for
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Positivity of the basic hypergeometric series and the MacMahon identity
Alexandr Garbali
The basic hypergeometric series whose upper and lower parameters are non-negative integer powers of satisfying a certain constraint can be, after a normalisatio…
Rational symmetric functions from the Izergin-Korepin 19-vertex model
Alexandr Garbali, Weiying Guo, Michael Wheeler
Starting from the Izergin-Korepin 19-vertex model in the quadrant, we introduce two families of rational multivariate functions and ; these are in direct analogy with fu…
Symmetric functions from the six-vertex model in half-space
Alexandr Garbali, Jan de Gier, William Mead +1
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commuta…
Modified Macdonald polynomials and integrability
Alexandr Garbali, Michael Wheeler
We derive combinatorial formulae for the modified Macdonald polynomial using coloured paths on a square lattice with quasi-cylindrical boundary conditions. The derivat…