Related papers: Row-strict dual immaculate functions
Symmetric function theory is a key ingredient in the Schubert calculus of Grassmannians. Quasisymmetric functions are analogues that are similarly central to algebraic combinatorics, but for which the associated geometry is poorly…
Petrie symmetric functions $G(k,n)$, also known as truncated homogeneous symmetric functions or modular complete symmetric functions, form a class of symmetric functions interpolating between the elementary symmetric functions $e_n$ and the…
Two criteria for the robust quasiconvexity of lower semicontinuous functions are established in terms of Fr\'echet subdifferentials in Asplund spaces.
In 1993 Delest and F\'edou showed that a generating function for connected skew shapes is given as a ratio $J_{\nu+1}/J_{\nu}$ of the Hahn--Exton $q$-Bessel functions when a parameter $\nu$ is zero. They conjectured that when $\nu$ is a…
The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by $1$ on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\{( \lambda_{1}+r\lambda_{2} ,r\lambda_{1}\lambda_{2}):…
We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. By constructing a graph on ribbon…
A production function $f$ is called quasi-sum if there are strict monotone functions $F, h_1,...,h_n$ with $F'>0$ such that $$f(x)= F(h_1 (x_1)+...+h_n (x_n)).$$ The justification for studying quasi-sum production functions is that these…
Given an element in a finite-dimensional real vector space, $V$, that is a nonnegative linear combination of basis vectors for some basis $B$, we compute the probability that it is furthermore a nonnegative linear combination of basis…
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…
We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic…
Consider the algebra Q<<x_1,x_2,...>> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant…
We obtain Hamel--Goulden-type ribbon decomposition determinantal formulas for flagged supersymmetric Schur functions. As an application, we derive corresponding new determinantal formulas dual refined canonical stable Grothendieck…
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…
By establishing relations between operators on compositions, we show that the posets of compositions arising from the right and left Pieri rules for noncommutative Schur functions can each be endowed with both the structure of dual graded…
It has been understood that correlation functions of multi-trace operators in ${\cal N}=4$ SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand such algebras have been known to…
We consider functions of natural numbers which allow a combinatorial interpretation as density functions (speed) of classes of relational structures, s uch as Fibonacci numbers, Bell numbers, Catalan numbers and the like. Many of these…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically…
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…
In \cite{HRW15}, Haglund, Remmel, Wilson state a conjecture which predicts a purely combinatorial way of obtaining the symmetric function $\Delta_{e_k}e_n$. It is called the Delta Conjecture. It was recently proved in \cite{GHRY} that the…