Related papers: A Shifted Parking Function Symmetric Function
We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted…
We extend the definition of weak symmetric continuity to be applicable for functions defined on any nonempty subset of $\R$. Then we investigate basic properties of weakly symmetrically continuous functions and compare them with those of…
This paper contains a partial answer to the open problem 3.11 of \cite{[H2008]}. That is to find an explicit bijection on Schr\"oder paths that inverts the statistics area and bounce. This paper started as an attempt to write the sum over…
Physical systems with symmetries are described by functions containing kinematical and dynamical parts. We consider the case when kinematical symmetries are described by a noncompact semisimple real Lie group $G$. Then separation of…
We introduce interpolation analogues of Schur Q-functions - the multiparameter Schur Q-functions. We obtain for them several results: a combinatorial formula, generating functions for one-row and two-rows functions, vanishing and…
Having a function $f$ and a set of functionals $\{\mathcal{C}_{n}\}$, $c_n^f \equiv \mathcal{C}_n \left(f\right)$, one can interpret function approximation very generally as a construction of some function $\mathcal{A}_{N}^{f}$ such that…
We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderon-Lozanovskii spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the…
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…
We study the asymptotic behavior of cycles of uniformly random parking functions. Our results are multifold: we obtain an explicit formula for the number of parking functions with a prescribed number of cyclic points and show that the…
We study Schroder paths drawn in a (m,n) rectangle, for any positive integers m and n. We get explicit enumeration formulas, closely linked to those for the corresponding (m,n)-Dyck paths. Moreover we study a Schroder version of…
We define a switch function to be a function from an interval to $\{1,-1\}$ with a finite number of sign changes. (Special cases are the Walsh functions.) By a topological argument, we prove that, given $n$ real-valued functions, $f_1,…
We define a new family of symmetric functions which are affine analogues of Stanley symmetric functions. We establish basic properties of these functions including symmetry, dominance and conjugation. We conjecture certain positivity…
On the set $\mathcal M$ of mean functions the symmetric mean of $M$ with respect to mean $M_0$ can be defined in several ways. The first one is related to the group structure on $\mathcal M$ and the second one is defined trough Gauss'…
The action of the symmetric group $S_n$ on the set $Park_n$ of parking functions of size $n$ has received a great deal of attention in algebraic combinatorics. We prove that the action of $S_n$ on $Park_n$ extends to an action of $S_{n+1}$.…
In a recent paper J. Haglund showed that a certain symmetric function expresion enumerates by t^{area} q^{dinv} of the parking functions whose diagonal word is in the shuffle of 12...j and j+1...j+n with k of the cars j+1,...,j+n in the…
The notion of parking sequences is a new generalization of parking functions introduced by Ehrenborg and Happ. In the parking process defining the classical parking functions, instead of each car only taking one parking space, we allow the…
We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
S-metric and b-metric spaces are metrizable, but it is still quite impossible to get an explicit form of the concerned metric function. To overcome this, the notion of $\phi$-metric is developed by making a suitable modification in triangle…
A symmetric variant of Shannon capacity is defined and computed.