Related papers: Partial Parking Functions
In 1980, Edelman defined a poset on objects called the noncrossing 2-partitions. They are closely related with noncrossing partitions and parking functions. To some extent, his definition is a precursor of the parking space theory, in the…
Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This…
By considering labeled configurations of ``bounded multiplicity'', one can construct a functor that fits between homology and stable homotopy. Based on previous work, we are able to give an equivalent description of this labeled…
We study Karoubian tensor categories which interpolate representation categories of families of so-called easy quantum groups in the same sense in which Deligne's interpolation categories $\mathrm{\underline{Rep}}(S_t)$ interpolate the…
A depth-first search version of Dhar's burning algorithm is used to give a bijection between the parking functions of a graph and labeled spanning trees, relating the degree of the parking function with the number of inversions of the…
Occupation probabilities for primary-secondary-primary cell strings and correlation functions for primary sites of a decorated lattice model are expressed through the well-studied partition function and correlation functions of the Ising…
We present the explicit forms of supergravity solutions for the various intersecting two BPS branes in eleven and ten dimensions, where one brane is localized at the delocalized other brane. Our partially localized supergravity solutions…
We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results…
For one-matrix models with polynomial potentials, the explicit relationship between the partition function and the isomonodromic tau function for the 2x2 polynomial differential systems satisfied by the associated orthogonal polynomials is…
In geometric, algebraic, and topological combinatorics, the unimodality of combinatorial generating polynomials is frequently studied. Unimodality follows when the polynomial is (real) stable, a property often deduced via the theory of…
Under a certain condition A we give a construction to calculate the intersection cohomology of a rank one local system on the complement to a hyperplane-like divisor
We construct a family of solvable lattice models whose partition functions include $p$-adic Whittaker functions for general linear groups from two very different sources: from Iwahori-fixed vectors and from metaplectic covers. Interpolating…
In these notes we show that any projective subspace arrangement can be realized as a generalized star configuration variety. This type of interpolation result may be useful in designing linear codes with prescribed codewords of minimum…
For any irreducible real reflection group $W$ with Coxeter number $h$, Armstrong, Reiner, and the author introduced a pair of $W \times \ZZ_h$-modules which deserve to be called {\sf $W$-parking spaces} which generalize the type A notion of…
The minimal model program suggests a compactification of the moduli space of hyperplane arrangements which is a moduli space of stable pairs. Here, a stable pair consists of a scheme X which is a degeneration of projective space and a…
We extend the Shi bijection from the Borel subalgebra case to parabolic subalgebras. In the process, the $I$-deleted Shi arrangement $\texttt{Shi}(I)$ naturally emerges. This arrangement interpolates between the Coxeter arrangement…
We propose to use the identification of topological string partition functions as equivariant indices on framed moduli spaces of instantons to study the Gopakumar-Vafa conjecture for some local Calabi-Yau geometries.
We characterize $q$-ample Ulrich bundles on a variety $X \subseteq \mathbb P^N$ with respect to $(q+1)$-dimensional linear spaces contained in $X$.
The transparent way for the invariant (Hamiltonian) description of equivariant localization of the integrals over phase space is proposed. It uses the odd symplectic structure, constructed over tangent bundle of the phase space and permits…
In this paper, norm estimates are obtained for the problem of minimal-norm tangential interpolation by vector-valued analytic functions in weighted H^p spaces, expressed in terms of the Carleson constants of related scalar measures.…