2 citations · 2 across the 8 of their papers we have counts for
8 papers
On equidistribution theorem for plane partitions
Alimzhan Amanov, Damir Yeliussizov
We prove equidistribution of two pairs of statistics on boxed plane partitions: (volume, trace) and (corner-hook volume, number of corners). The proof relies on different 3d visual…
Group and algebra hyperdeterminant
Alimzhan Amanov
In 1896, Dedekind posed the problem of factoring the group determinant in the non-abelian case to Frobenius, whose solution sparked the birth of finite-group representation theory.…
Highest weight vectors of tensors
Alimzhan Amanov, Damir Yeliussizov
We study highest weight vectors for symmetric and alternating spaces of tensors, whose dimensions are given by generalized Kronecker coefficients. We describe the algebraic relatio…
Some unimodal sequences of Kronecker coefficients
Alimzhan Amanov, Damir Yeliussizov
We conjecture unimodality for some sequences of generalized Kronecker coefficients and prove it for partitions with at most two columns. The proof is based on a hard Lefschetz prop…
Fundamental invariants of tensors, Latin hypercubes, and rectangular Kronecker coefficients
Alimzhan Amanov, Damir Yeliussizov
We study polynomial SL-invariants of tensors, mainly focusing on fundamental invariants which are of smallest degrees. In particular, we prove that certain 3-dimensional analogue o…
Tensor slice rank and Cayley's first hyperdeterminant
Alimzhan Amanov, Damir Yeliussizov
Cayley's first hyperdeterminant is a straightforward generalization of determinants for tensors. We prove that nonzero hyperdeterminants imply lower bounds on some types of tensor…
MacMahon's statistics on higher-dimensional partitions
Alimzhan Amanov, Damir Yeliussizov
We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between -dimensional partitions and …
Determinantal formulas for dual Grothendieck polynomials
Alimzhan Amanov, Damir Yeliussizov
We prove Jacobi-Trudi-type determinantal formulas for skew dual Grothendieck polynomials which are -theoretic deformations of Schur polynomials. We also prove a bialternant-type…