36 citations · 67 across the 18 of their papers we have counts for
20 papers · 1 filter
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…
Inhomogeneous -Whittaker polynomials II: ring theorem and positive specializations
Ajeeth Gunna, Damir Yeliussizov
We study inhomogeneous -Whittaker polynomials which extend both -Whittaker and stable Grothendieck polynomials. We prove that inhomogeneous -Whittaker polynomials (in coun…
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…
Bounds on the number of higher-dimensional partitions
Damir Yeliussizov
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.
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…
Saturation of Rota's basis conjecture
Damir Yeliussizov
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.
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…
Dual Grothendieck polynomials via last-passage percolation
Damir Yeliussizov
The ring of symmetric functions has a basis of dual Grothendieck polynomials that are inhomogeneous -theoretic deformations of Schur polynomials. We prove that dual Grothendieck…
Enumeration of plane partitions by descents
Damir Yeliussizov
We study certain bijection between plane partitions and -matrices. As applications, we prove a Cauchy-type identity for generalized dual Grothendieck polynomials. We in…
Random plane partitions and corner distributions
Damir Yeliussizov
We explore some probabilistic applications arising in connections with -theoretic symmetric functions. For instance, we determine certain corner distributions of random lozenge…
Positive specializations of symmetric Grothendieck polynomials
Damir Yeliussizov
It is a classical fundamental result that Schur-positive specializations of the ring of symmetric functions are characterized via totally positive functions whose parametrization d…
On the largest Kronecker and Littlewood--Richardson coefficients
Igor Pak, Greta Panova, Damir Yeliussizov
We give new bounds and asymptotic estimates for Kronecker and Littlewood--Richardson coefficients. Notably, we resolve Stanley's questions on the shape of partitions attaining the…
Symmetric Grothendieck polynomials, skew Cauchy identities, and dual filtered Young graphs
Damir Yeliussizov
Symmetric Grothendieck polynomials are analogues of Schur polynomials in the K-theory of Grassmannians. We build dual families of symmetric Grothendieck polynomials using Schur ope…
Duality and deformations of stable Grothendieck polynomials
Damir Yeliussizov
Stable Grothendieck polynomials can be viewed as a K-theory analog of Schur polynomials. We extend stable Grothendieck polynomials to a two-parameter version, which we call canonic…
Lattice Path Matroids: Negative Correlation and Fast Mixing
Emma Cohen, Prasad Tetali, Damir Yeliussizov
Catalan numbers arise in many enumerative contexts as the counting sequence of combinatorial structures. In this work, we consider natural Markov chains on some of the realizations…
Path decompositions of digraphs and their applications to Weyl algebra
Askar Dzhumadil'daev, Damir Yeliussizov
We consider decompositions of digraphs into edge-disjoint paths and describe their connection with the -th Weyl algebra of differential operators. This approach gives a graph-th…
Stirling permutations on multisets
Askar Dzhumadil'daev, Damir Yeliussizov
A permutation of a multiset is called Stirling permutation if as soon as and In our paper we study Stirling polynomials that arise in the ge…