Related papers: Pak-Stanley labeling for Central Graphical Arrange…
We consider the internalization of the usual notion of principal bundle in a site that has all pullbacks and a terminal object. We use this notion to consider the explicit construction of quotient prestacks via presheaves of categories of…
In line with the recent development in topological graph theory, we are considering undirected graphs that are allowed to contain {\em multiple edges}, {\em loops}, and {\em semi-edges}. A graph is called {\em simple} if it contains no…
We established a hyperplane restriction theorem for the local holomorphic mappings between projective spaces, which is inspired by the corresponding theorem of Green for homogeneous ideals in polynomial rings. Our theorem allows us to give…
A split graph is a graph whose vertices can be partitioned into a clique and a stable set. We investigate the combinatorial species of split graphs, providing species-theoretic generalizations of enumerative results due to B\'ina and…
In this paper we introduce trajectory-based labeling, a new variant of dynamic map labeling, where a movement trajectory for the map viewport is given. We define a general labeling model and study the active range maximization problem in…
The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle $E(B,V,A)$ associated to a quantum principal bundle $P(B,A)$ are in…
Hetyei introduced in 2019 the homogenized Linial arrangement and showed that its regions are counted by the median Genocchi numbers. In the course of devising a different proof of Hetyei's result, Lazar and Wachs considered another…
Generalized splines are a simultaneous generalization of GKM theory -- which studies equivariant cohomology -- and classical splines, which provide piecewise approximations of functions. Generalized splines can also be understood via…
We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitary face structure, and (ii) (weighted) non-oriented maps with exactly one face. Above, each non-oriented map…
In 1999, Pitman and Stanley introduced the polytope bearing their name along with a study of its faces, lattice points, and volume. The Pitman-Stanley polytope is well-studied due to its connections to probability, parking functions, the…
We introduce the class of interval $H$-graphs, which is the generalization of interval graphs, particularly interval bigraphs. For a fixed graph $H$ with vertices $a_1,a_2,\dots,a_k$, we say that an input graph $G$ with given partition…
Weakly supervised learning with only coarse labels can obtain visual explanations of deep neural network such as attention maps by back-propagating gradients. These attention maps are then available as priors for tasks such as object…
Given an undirected graph $G=(V,E)$, and a designated vertex $q\in V$, the notion of a $G$-parking function (with respect to $q$) was independently developed and studied by various authors, and has recently gained renewed attention. This…
Poor generalization is one symptom of models that learn to predict target variables using spuriously-correlated image features present only in the training distribution instead of the true image features that denote a class. It is often…
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…
The number of regions of the type A_{n-1} Shi arrangement in R^n is counted by the intrinsically beautiful formula (n+1)^{n-1}. First proved by Shi, this result motivated Pak and Stanley as well as Athanasiadis and Linusson to provide…
The point-line geometry known as a \textit{partial quadrangle} (introduced by Cameron in 1975) has the property that for every point/line non-incident pair $(P,\ell)$, there is at most one line through $P$ concurrent with $\ell$. So in…
In this paper firstly, we generalize the concept of codismantlable graphs to hypergraphs and show that some special vertex decomposable hypergraphs are codismantlable. Then we generalize the concept of bouquet in graphs to hypergraphs to…
Hypermaps were introduced as an algebraic tool for the representation of embeddings of graphs on an orientable surface. Recently a bijection was given between hypermaps and indecomposable permutations; this sheds new light on the subject by…
The discriminantal arrangement $\mathcal{B}(n,k,\mathcal{A})$ has been introduced by Manin and Schectman in 1989 and it consists of all non-generic translates of a generic arrangement $\mathcal{A}$ of n hyperplanes in a $k$-dimensional…