12 citations · 26 across the 16 of their papers we have counts for
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Askey--Wilson polynomials with ASEP parameters
Younggwang Cho, Donghyun Kim, Jang Soo Kim
Koornwinder moments generalize the Askey--Wilson moments arising in the asymmetric simple exclusion process. Rains conjectured that, under the specialization , the minimal num…
An explicit formula for Koornwinder moments and Rains' positivity conjecture
Younggwang Cho, Donghyun Kim, Jang Soo Kim +3
The asymmetric simple exclusion process (ASEP) is an important particle model with deep connections to orthogonal polynomials. Motivated by this connection, Corteel and Williams in…
Shuffle formula in science fiction for Macdonald polynomials
Donghyun Kim, Seung Jin Lee, Jaeseong Oh
We initiate the study of the Macdonald intersection polynomials , which are indexed by -tuples of partitions $μ^{(1)},\dots,μ^{(…
Toward Butler's conjecture
Donghyun Kim, Seung Jin Lee, Jaeseong Oh
For a partition , let be two distinct partitions such that . Butler conjectured that the divided difference $\operatorname{I}_{λ,μ}[X;q,t]=(T_λ\w…
Techniques in equivariant Ehrhart theory
Sophia Elia, Donghyun Kim, Mariel Supina
Equivariant Ehrhart theory generalizes the study of lattice point enumeration to also account for the symmetries of a polytope under a linear group action. We present a catalogue o…
Negative moments of orthogonal polynomials
Jihyeug Jang, Donghyun Kim, Jang Soo Kim +2
If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurr…
Schubert polynomials, the inhomogeneous TASEP, and evil-avoiding permutations
Donghyun Kim, Lauren Williams
Consider a lattice of n sites arranged around a ring, with the sites occupied by particles of weights ; the possible arrangements of particles in sites thus co…
Schubert polynomials and the inhomogeneous TASEP on a ring
Donghyun Kim, Lauren Williams
Consider a lattice of n sites arranged around a ring, with the sites occupied by particles of weights ; the possible arrangements of particles in sites thus co…
Combinatorial formulas for the coefficients of the Al-Salam-Chihara polynomials
Donghyun Kim
The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable depending on 3 parameters , and . They are closely connected to a m…
A combinatorial formula for the Ehrhart -vector of the hypersimplex
Donghyun Kim
We give a combinatorial formula for the Ehrhart -vector of the hypersimplex. In particular, we show that is the number of hypersimplicial decorated ordere…