Related papers: Lenart's bijection via bumpless pipe dreams

Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We…

We answer four questions from a recent paper of Rao and Shinkar on Lipschitz bijections between functions from $\{0,1\}^n$ to $\{0,1\}$. (1) We show that there is no $O(1)$-bi-Lipschitz bijection from $\mathrm{Dictator}$ to $\mathrm{XOR}$…

Advancing the sparse regularity method, we prove one-sided and two-sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results of Conlon, Fox and Zhao [Adv. Math. 256 (2014), 206--290]. These inheritance…

Let $n$ be a positive integer and $H$ a Hilbert space. The description of the general form of bijective maps on the set of $n$-dimensional subspaces of $H$ preserving the maximal principal angle has been obtained recently. This is a…

We give a bijective proof of Macdonald's reduced word identity using pipe dreams and Little's bumping algorithm. This proof extends to a principal specialization due to Fomin and Stanley. Such a proof has been sought for over 20 years. Our…

In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily…

Learning vectorized embeddings is fundamental to many recommender systems for user-item matching. To enable efficient online inference, representation binarization, which embeds latent features into compact binary sequences, has recently…

Let $M$ be a holomorphically symplectic complex manifold, not necessarily compact or quasiprojective, and $X \subset M$ a compact Lagrangian submanifold. We construct a deformation to the normal cone, showing that a neighbourhood of $X$ can…

Working over a field of characteristic other than $2$, we examine a relationship between quadrilaterals and the pencil of conics passing through their vertices. Asymptotically, such a pencil of conics is what we call a bisector field, a set…

Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane…

The purpose of this note is to attract attention to the following conjecture (metastable $r$-fold Whitney trick) by clarifying its status as not having a complete proof, in the sense described in the paper. Assume that…

We define bidual bounded $uo$-convergence in vector lattices and investigate relations between this convergence and $b$-property. We prove that for a regular Riesz dual system $\langle X,X^{\sim}\rangle$, $X$ has $b$-property if and only if…

A sub-problem of the open problem of finding an explicit bijection between alternating sign matrices and totally symmetric self-complementary plane partitions consists in finding an explicit bijection between so-called $(n,k)$ Gog…

Let $G = (V,E)$ be a simple finite graph. The corresponding bunkbed graph $G^\pm$ consists of two copies $G^+ = (V^+,E^+),G^- = (V^-,E^-)$ of $G$ and additional edges connecting any two vertices $v_+ \in V_+,v_- \in V_-$ that are the copies…

In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulated [2] another combinatorial conjecture (Conjecture 3);…

We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem---to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph---and…

Phylogenetic trees are binary nonplanar trees with labelled leaves, and plane oriented recursive trees are planar trees with an increasing labelling. Both families are enumerated by double factorials. A bijection is constructed, using the…

Let $X$ be a closed semialgebraic set of dimension $k.$ If $n\ge 2k+1$, then there is a bi-Lipschitz and semialgebraic embedding of $X$ into $\Bbb R^n.$ Moreover, if $n \ge 2k+2$, then this embedding is unique (up to a bi-Lipschitz and…

We define bileptons to be bosons coupling to a pair of leptons and construct the most general dimension four lagrangian involving scalar and vector bileptons. We concentrate on fields with lepton number 2, and derive model independent…

We construct a bijection from permutations to some weighted Motzkin paths known as Laguerre histories. As one application of our bijection, a neat $q$-$\gamma$-positivity expansion of the $(\inv,\exc)$-$q$-Eulerian polynomials is obtained.