相关论文: Inverting the General Order Sweep Map
We develop a theory of $\times$-homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that $\times$-homotopies from finite graphs can be decomposed…
We generalize the shuffle theorem and its $(km,kn)$ version, as conjectured by Haglund et al. and Bergeron et al., and proven by Carlsson and Mellit, and Mellit, respectively. In our version the $(km,kn)$ Dyck paths on the combinatorial…
The paper studies the harmonic maps on a direction between a Riemannian space and a generalized Lagrange space. Also, it is proved there that the solutions of C^2 class of certain ODEs or PDEs are harmonic maps, in the sense of this paper.
Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes.…
We study the relationship between rational slope Dyck paths and invariant subsets of $\mathbb Z,$ extending the work of the first two authors in the relatively prime case. We also find a bijection between $(dn,dm)$--Dyck paths and…
In an effort to further understanding $q,t$-Catalan statistics, a new statistic on Dyck paths called $\mathtt{depth}$ was proposed in Pappe, Paul and Schilling (2022) and was shown to be jointly equi-distributed with the well-known…
Neural network systems describe complex mappings that can be very difficult to understand. In this paper, we study the inverse problem of determining the input images that get mapped to specific neural network classes. Ultimately, we expect…
This paper develops an infinitesimal order of magnitude coupled with overflow technique that allows nonnumerical proofs of nondegenerate and degenerate inverse mapping theorems for mappings minimally regular at a point. This approach is…
We introduce the notion of fully simple maps, which are maps with non self-intersecting disjoint boundaries. In contrast, maps where such a restriction is not imposed are called ordinary. We study in detail the combinatorics of fully simple…
The well-known $q,t$-Catalan sequence has two combinatorial interpretations as weighted sums of ordinary Dyck paths: one is Haglund's area-bounce formula, and the other is Haiman's dinv-area formula. The zeta map was constructed to connect…
A map is \emph{vertex-reversing} if it admits an arc-transitive automorphism group with dihedral vertex stabilizers. This paper classifies solvable vertex-reversing maps whose edge number and Euler characteristic are coprime. The…
In this paper, we consider the possible types of regular maps of order $2^n$, where the order of a regular map is the order of automorphism group of the map. For $n \le 11$, M. Conder classified all regular maps of order $2^n$. It is easy…
We propose efficient algorithms for enumerating the notorious combinatorial structures of maximal planar graphs, called canonical orderings and Schnyder woods, and the related classical graph drawings by de Fraysseix, Pach, and Pollack…
This paper is concerned with so-called index $d$ generalized cyclotomic mappings of a finite field $\mathbb{F}_q$, which are functions $\mathbb{F}_q\rightarrow\mathbb{F}_q$ that agree with a suitable monomial function $x\mapsto ax^r$ on…
Motivated by the works of Wang and Liu [Linear Algebra Appl., 488 (2016) 235-248; MR3419784] and Mosic [Results Math., 75(2) (2020) 1-21; MR4079761], we provide further results on GD inverses and introduce two new classes for square…
In this article we propose a general transformation for decorated spin models. The advantage of this transformation is to perform a direct mapping of a decorated spin model onto another effective spin thus simplifying algebraic computations…
The canonical tree-decomposition theorem, given by Robertson and Seymour in their seminal graph minors series, turns out to be one of the most important tool in structural and algorithmic graph theory. In this paper, we provide the…
Applying a method of Godsil and McKay \cite{GM} to some graphs related to the symplectic graph, a series of new infinite families of strongly regular graphs with parameters…
For a natural class of $r \times n$ integer matrices, we construct a non-convex polytope which periodically tiles $\mathbb R^n$. From this tiling, we provide a family of geometrically meaningful maps from a generalized sandpile group to a…
If a graph $G_M$ is embedded into a closed surface $S$ such that $S \backslash G_M$ is a collection of disjoint open discs, then $M=(G_M,S)$ is called a {\em map}. A {\em zigzag} in a map $M$ is a closed path which alternates choosing, at…