Related papers: Symplectic Q-functions
A motivation comes from {\em M. Ismail and et al.: A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77--84} to study a generalization of close-to-convex functions by means of a $q$-analog of a difference…
The machinery of noncommutative Schur functions is a general approach to Schur positivity of symmetric functions initiated by Fomin-Greene. Hwang recently adapted this theory to posets to give a new approach to the Stanley-Stembridge…
q-Supernomial coefficients are generalizations of the q-binomial coefficients. They can be defined as the coefficients of the Hall-Littlewood symmetric function in a product of the complete symmetric functions or the elementary symmetric…
In [arXiv:2107.01437], the authors studied the mean-square of certain sums of the divisor function $d_k(f)$ over the function field $\mathbb{F}_q[T]$ in the limit as $q \to \infty$ and related these sums to integrals over the ensemble of…
We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…
The Macdonald symmetric functions are used to define measures on the set of all partitions of all integers. Probabilistic algorithms are given for growing partitions according to these measures. The case of Hall-Littlewood polynomials is…
We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. This expansion follows from several new…
In our joint paper with W. Fulton (math.AG/9804041) we prove a formula for the cohomology class of a quiver variety. This formula is general enough to give new expressions for all known types of Schubert polynomials. In the present paper we…
The purpose of this note is to introduce a new family of quasi-symmetric functions called LLT cumulants and discuss its properties. We define LLT cumulants using the algebraic framework for conditional cumulants and we prove that the…
We explore a number of functional properties of the $q$-gamma function and a class of its quotients; including the $q$-beta function. We obtain formulas for all higher logarithmic derivatives of these quotients and give precise conditions…
We establish new Murnaghan--Nakayama rules for symplectic, orthogonal and orthosymplectic Schur functions. The classical Murnaghan--Nakayama rule expresses the product of a power sum symmetric function with a Schur function as a linear…
We give a proof of the generalized Cauchy identity for double Grothendieck polynomials, a combinatorial interpretation of the stable double Grothendieck polynomials in terms of triples of tableaux, and an interpolation between the stable…
We define analogue of theta-functions on the Kodaira--Thurston manifold which is a compact 4-dimensional symplectic manifold and use them to construct canonical symplectic embedding of the Kodaira--Thurston manifold into the complex…
This paper is to characterize piecewise continuous almost periodic functions as the product of Bohr almost periodic functions and sequences. As an application, the result is used to discuss piecewise continuous almost periodic solutions of…
We consider the group $\mathrm{Aut}(T)$ of isometries of a semi-homogeneous tree $T=T_{q_+,q_-}$ with valencies $q_+ +1$ and $q_- +1$ and its two orbits $V_+$, $V_-$ respectively. We make use of the action of $\mathrm{Aut} (T)$ to equip the…
The $K$-theoretic Schur $P$- and $Q$-functions $GP_\lambda$ and $GQ_\lambda$ may be concretely defined as weight generating functions for semistandard shifted set-valued tableaux. These symmetric functions are the shifted analogues of…
In this paper, we define a q-adic factorial and we demonstrate some properties of a generalized p-adic gamma function. Also, some numerical examples have been given
This is a survey about certain "almost homomorphisms" and "almost linear" functionals (called quasi-morphisms and quasi-states) in symplectic topology and their applications to Hamiltonian dynamics, functional-theoretic properties of…
We show the equivalence of the Pieri formula for flag manifolds and certain identities among the structure constants, giving new proofs of both the Pieri formula and of these identities. A key step is the association of a symmetric function…
In this paper, we explore a consequence of symplectic duality (also known as 3d mirror symmetry) in the setting of enumerative geometry. The theory of quasimaps allows one to associate hypergeometric functions called vertex functions to…