Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Yeliussizov, Damir"'
We study random permutations arising from reduced pipe dreams. Our main model is motivated by Grothendieck polynomials with parameter $\beta=1$ arising in K-theory of the flag variety. The probability weight of a permutation is proportional to the pr
Externí odkaz:
http://arxiv.org/abs/2407.21653
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
Autor:
Yeliussizov, Damir
We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.
Externí odkaz:
http://arxiv.org/abs/2302.04799
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
Autor:
Yeliussizov, Damir
We prove an asymptotic saturation-type version of Rota's basis conjecture. It relies on the connection of Tao's slice rank with unstable tensors from geometric invariant theory.
Externí odkaz:
http://arxiv.org/abs/2107.12926
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
Autor:
Yeliussizov, Damir
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G8, Pp 1367-1373 (2023)
We show that the Levi-Civita tensors are semistable in the sense of Geometric Invariant Theory, which is equivalent to an analogue of the Alon–Tarsi conjecture on Latin squares. The proof uses the connection of Tao’s slice rank with semistable te
Externí odkaz:
https://doaj.org/article/d1ce0fed13b943f99b967b0c6eb9cc7a
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
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
Autor:
Yeliussizov, Damir
The ring of symmetric functions has a basis of dual Grothendieck polynomials that are inhomogeneous $K$-theoretic deformations of Schur polynomials. We prove that dual Grothendieck polynomials determine column distributions for a directed last-passag
Externí odkaz:
http://arxiv.org/abs/2002.10086