Related papers: Jack polynomials for the $BC_n$ root system and ge…
We give the explicit analytic development of any Jack or Macdonald polynomial in terms of elementary (resp. modified complete) symmetric functions. These two developments are obtained by inverting the Pieri formula.
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.
3D (3 dimensional) Young diagrams are a generalization of 2D Young diagrams. In this paper, We consider 3D Bosons and 3-Jack polynomials. We associate three parameters $h_1,h_2,h_3$ to $y,x,z$-axis respectively. 3-Jack polynomials are…
We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack…
We consider two important families of BC_n-symmetric polynomials, namely Okounkov's interpolation polynomials and Koornwinder's orthogonal polynomials. We give a family of difference equations satisfied by the former, as well as…
Symmetric Jack polynomials arise naturally in several contexts, including statistics, physics, combinatorics, and representation theory. They are pairwise orthogonal with repsect to two different inner products, the first defined by…
Functions like the exponential, Chebyshev polynomials, and monomial symmetric polynomials are preeminent among all special functions. They have simple definitions and can be expressed using easily specified integers like n!. Families of…
In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are…
This article is devoted to the study of Jack connection coefficients, a generalization of the connection coefficients of the classical commutative subalgebras of the group algebra of the symmetric group closely related to the theory of Jack…
Using the ground state $\psi_0$ of a multicomponent generalization of the Calogero-Sutherland model as a weight function, orthogonal polynomials in the coordinates of one of the species are constructed. Using evidence from exact analytic…
The theory of non-symmetric Jack polynomials is developed independently of the theory of symmetric Jack polynomials, and this theory together with the relationship between the non-symmetric, symmetric and anti-symmetric Jack polynomials is…
We present a general survey of some recent developments regarding the construction of compact quantum symmetric spaces and the analysis of their zonal spherical functions in terms of $q$-orthogonal polynomials. In particular, we define a…
We derive a generalized Rogers generating function and corresponding definite integral, for the continuous $q$-ultraspherical polynomials by applying its connection relation and utilizing orthogonality. Using a recent generalization of the…
We find a biorthogonal expansion of the Cayley transform of the non-symmetric Jack functions in terms of the non-symmetric Jack polynomials, the coefficients being Meixner-Pollaczek type polynomials. This is done by computing the…
Jack characters are a generalization of the characters of the symmetric groups; a generalization that is related to Jack symmetric functions. We investigate the structure coefficients for Jack characters; they are a generalization of the…
We call superpartitions the indices of the eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model. We obtain an ordering on superpartitions from the explicit action of the model's Hamiltonian on…
In this paper, we study Grothendieck polynomials from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials, analogues of the factorial Schur functions and present some of their properties, and use them to produce a…
In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend…
In previous work of the first and third authors, we proposed a conjecture that the Kauffman bracket skein module of any knot in $S^3$ carries a natural action of the rank 1 double affine Hecke algebra $SH_{q,t_1, t_2}$ depending on 3…