Related papers: Bijectivity of a generalized Pak-Stanley labeling

A k-triangulation of a convex polygon is a maximal set of diagonals so that no k+1 of them mutually cross in their interiors. We present a bijection between 2-triangulations of a convex n-gon and pairs of non-crossing Dyck paths of length…

Let $X$ be a complex projective variety defined over $\mathbb R$. Recently, Bernardi and the first author introduced the notion of admissible rank with respect to $X$. This rank takes into account only decompositions that are stable under…

In this series of articles we study connections between combinatorics of multidimensional generalizations of Cauchy identity and continuous objects such as multidimensional Brownian motions and Brownian bridges. In Part I of the series we…

We study preorders on (equivalence classes of) maximal chains in the general context of polygonal lattices endowed with suitably nice edge labellings. We show that, given a quotient of polygonal lattices, such edge labellings descend to the…

We introduce an object called a tree growing sequence (TGS) in an effort to generalize bijective correspondences between $G$-parking functions, spanning trees, and the set of monomials in the Tutte polynomial of a graph $G$. A tree growing…

This paper primarily investigates a specific type of deformation of the braid arrangement $\mathcal{B}_n$ in $\mathbb{R}^n$, denoted by $\mathcal{B}_n^A$ and defined in (1.2). Let $r_l(\mathcal{B}_n^A)$ be the number of regions of level $l$…

Let $G$ be a connected finite graph. Backman, Baker, and Yuen have constructed a family of explicit and easy-to-describe bijections $g_{\sigma,\sigma^*}$ between spanning trees of $G$ and $(\sigma,\sigma^*)$-compatible orientations, where…

We study stratification, that is the classification of localizing tensor ideal subcategories by geometric means, in the context of Kasparov's equivariant KK-theory of C*-algebras. We introduce a straightforward countable analog of the…

We show that the members of a large class of unbalanced four-manifold trisections are standard, and we present a family of trisections that is likely to include non-standard trisections of the four-sphere. As an application, we prove a…

We extend the notion of parking function polytopes and study their geometric and combinatorial structure, including normal fans, face posets, and $h$-polynomials, as well as their connections to other classes of polytopes. To capture their…

The enumeration of linear $\lambda$-terms has attracted quite some attention recently, partly due to their link to combinatorial maps. Zeilberger and Giorgetti (2015) gave a recursive bijection between planar linear normal $\lambda$-terms…

The braid arrangement is the Coxeter arrangement of the type $A_\ell$. The Shi arrangement is an affine arrangement of hyperplanes consisting of the hyperplanes of the braid arrangement and their parallel translations. In this paper, we…

We consider maps on orientable surfaces. A map is called \emph{unicellular} if it has a single face. A \emph{covered map} is a map (of genus $g$) with a marked unicellular spanning submap (which can have any genus in $\{0,1,...,g\}$). Our…

The key to multi-label image classification (MLC) is to improve model performance by leveraging label correlations. Unfortunately, it has been shown that overemphasizing co-occurrence relationships can cause the overfitting issue of the…

Let Spec(A) be an affine derived stack. We give two proofs of the existence of a canonical map from the moduli space of shifted Poisson structures (in the sense of Pantev-To\"en-Vaqui\'e-Vezzosi, see http://arxiv.org/abs/1111.3209 ) on…

The alternating sign matrices-descending plane partitions (ASM-DPP) bijection problem is one of the most intriguing open problems in bijective combinatorics, which is also relevant to integrable combinatorics. The notion of a signed set and…

In this paper we give a bijective proof for a relation between uni- bi- and tricellular maps of certain topological genus. While this relation can formally be obtained using Matrix-theory as a result of the Schwinger-Dyson equation, we here…

A union of an arrangement of affine hyperplanes $H$ in $R^d$ is the real algebraic variety associated to the principal ideal generated by the polynomial $p_{H}$ given as the product of the degree one polynomials which define the hyperplanes…

We investigate multi-label classification involving large sets of labels, where the output labels may be known to satisfy some logical constraints. We look at an architecture in which classifiers for individual labels are fed into an…

In this article we introduce generalized projective spaces (Definitions $[2.1, 2.5]$) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem $A$, the surjectivity of the Chinese remainder…