Related papers: Lenart's bijection via bumpless pipe dreams

A $d$-angulation is a planar map with faces of degree $d$. We present for each integer $d\geq 3$ a bijection between the class of $d$-angulations of girth $d$ (i.e., with no cycle of length less than $d$) and a class of decorated plane…

We prove a conjecture of J.-C. Novelli, J.-Y. Thibon, and L. K. Williams (2010) about an equivalence of two triples of statistics on permutations. To prove this conjecture, we construct a bijection through different combinatorial objects,…

We give some general results on proper-biharmonic submanifolds of a complex space form and, in particular, of the complex projective space. These results are mainly concerned with submanifolds with constant mean curvature or parallel mean…

Let $P$ be a planar $n$-gon with the sidelengths $a_1, \ldots, a_n$ and let us denote by $L=L(P)$ the corresponding planar polygonal linkage. We are concerned with the problem of finding conditions on the sidelengths $a_i$ which guarantee…

We present a general bijective approach to planar hypermaps with two main results. First we obtain unified bijections for all classes of maps or hypermaps defined by face-degree constraints and girth constraints. To any such class we…

A diffeological connection on a diffeological vector pseudo-bundle is defined just the usual one on a smooth vector bundle; this is possible to do, because there is a standard diffeological counterpart of the cotangent bundle. On the other…

In this paper we show the equivalence among three conjectures (and related open questions), namely, the embedding of univalent maps of the unit ball into Loewner chains, the approximation of univalent maps with entire univalent maps and the…

We propose a generalisation of Mori dream spaces to stacks. We show that this notion is preserved under root constructions and taking abelian gerbes. Unlike the case of Mori dream spaces, such a stack is not always given as a quotient of…

We describe how the result in [1] extends to prove the existence of a Serre type spectral sequence converging to the symplectic homology SH_*(M) of an exact Sub-Liouville domain M in a cotangent bundle T*N. We will define a notion of a…

We develop a new bijective framework for the enumeration of bipartite planar maps with control on the degree distribution of black and white vertices. Our approach builds on the blossoming-tree paradigm, introducing a family of orientations…

We present new links between some remarkable martingales found in the study of the Binary Search Tree, or of the Bisection Problem, looking at them on the probability space of a continuous time binary branching process.

We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by…

The non-convexity of a smooth and compact connected component of a real algebraic plane curve can be measured by a combinatorial object called the Poincare-Reeb tree associated to the curve and to a direction of projection. In this paper we…

Triangulations of the 5-gon with no separating triangle nor quadrangle, so called 5c-triangulations, are a planar map family closely related to 5-connected planar triangulations. We show that 5c-triangulations are in bijection with…

In arXiv:1905.07734 we presented a construction that is an analogue of Pontryagin's for proper maps in stable dimensions. This gives a bijection between the cobordism set of framed embedded compact submanifolds in $W\times\mathbb{R}^n$ for…

In this paper, we prove a result on the bisection of mass assignments by parallel hyperplanes on Euclidean vector bundles. Our methods consist of the development of a novel lifting method to define the configuration space--test map scheme,…

This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X-->V, and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a Banach space. Here, we consider the case…

Matchings are frequently used to model RNA secondary structures; however, not all matchings can be realized as RNA motifs. One class of matchings, called the L $\&$ P matchings, is the most restrictive model for RNA secondary structures in…

Postnikov gave a parametrization for the totally non-negative Grassmannian using the matroid decomposition and associating a network with \reflectbox{L}-diagrams. Talaska and Williams extend this result to the entire Grassmannian by using…

Set partitions avoiding $k$-crossing and $k$-nesting have been extensively studied from the aspects of both combinatorics and mathematical biology. By using the generating tree technique, the obstinate kernel method and Zeilberger's…