Related papers: Jack characters and enumeration of maps
We discuss the symmetric homogeneous polynomial solutions of the generalized Laplace's equation which arises in the context of the Calogero-Sutherland model on a line. The solutions are expressed as linear combinations of Jack polynomials…
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…
We study Jack polynomials in $N$ variables, with parameter $\alpha$, and having a prescribed symmetry with respect to two disjoint subsets of variables. For instance, these polynomials can exhibit a symmetry of type AS, which means that…
We define a class of bipartite graphs that correspond naturally with Ferrers diagrams. We give expressions for the number of spanning trees, the number of Hamiltonian paths when applicable, the chromatic polynomial, and the chromatic…
In this paper, Jack lemma is used for obtaining several differential inequalities over analytic functions that later on, lead to new criteria for univalency in the unit disk.
We investigate graphs that have characteristic-dependent well-covered dimension and show how more of these graphs can be constructed from known ones.
Refinements of the transchromatic generalized character maps are constructed by taking into account the torus action on the inertia groupoid (also known as the Fix functor). The relationship between this construction and the geometry of…
In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if $\{ G_ k \}_{k\geq 1}$ is a set of connected graphs such that $G_k$ has $k$ vertices for…
We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We obtain two explicit formulas for these polynomials: a $q$-integral representation and a combinatorial formula. Our main tool is…
We examine the role of character patterns in three tasks: morphological analysis, lemmatization and copy. We use a modified version of the standard sequence-to-sequence model, where the encoder is a pattern matching network. Each pattern…
We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack polynomials and Jack characters. We show that…
Companion matrices of the second type are characterized by properties that involve bilinear maps.
A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.
GAP functions are useful for solving optimization problems, but the literature contains a variety of different concepts of GAP functions. It is interesting to point out that these concepts have many similarities. Here we introduce…
Stanley and F\'eray gave a formula for the irreducible character of the symmetric group related to a multi-rectangular Young diagram. This formula shows that the character is a polynomial in the multi-rectangular coordinates and gives an…
The optimal calculation order of a computational graph can be represented by a set of algebraic expressions. Computational graph and algebraic expression both have close relations and significant differences, this paper looks into these…
We give the explicit analytic development of Macdonald polynomials in terms of "modified complete" and elementary symmetric functions. These expansions are obtained by inverting the Pieri formula. Specialization yields similar developments…
Through the theory of Jack polynomials we give an iterative method for integral formula of Dunkl-Bessel functions of type $A_{N-1}$ and a partial product formula for it.
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
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…