Výsledky vyhledávání - "Amanov, Alimzhan"

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Some unimodal sequences of Kronecker coefficients

Autor: Amanov, Alimzhan, Yeliussizov, Damir

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 property for corresponding highest weight spaces. We also study more gener

Externí odkaz: http://arxiv.org/abs/2312.17054

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Fundamental invariants of tensors, Latin hypercubes, and rectangular Kronecker coefficients

Autor: Amanov, Alimzhan, Yeliussizov, Damir

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 of the Alon--Tarsi conjecture on Latin cubes considered previously by B

Externí odkaz: http://arxiv.org/abs/2202.11059

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Tensor slice rank and Cayley's first hyperdeterminant

Autor: Amanov, Alimzhan, Yeliussizov, Damir

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 ranks. This result applies to the slice rank introduced by Tao and mor

Externí odkaz: http://arxiv.org/abs/2107.08864

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MacMahon's statistics on higher-dimensional partitions

Autor: Amanov, Alimzhan, Yeliussizov, Damir

We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between $d$-dimensional partitions and $d$-dimensional arrays of nonnegative integers. This bijection has a numb

Externí odkaz: http://arxiv.org/abs/2009.00592

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Determinantal formulas for dual Grothendieck polynomials

Autor: Amanov, Alimzhan, Yeliussizov, Damir

We prove Jacobi-Trudi-type determinantal formulas for skew dual Grothendieck polynomials which are $K$-theoretic deformations of Schur polynomials. We also prove a bialternant-type formula analogous to the classical definition of Schur polynomials.

Externí odkaz: http://arxiv.org/abs/2003.03907

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