Research
Research
Research
Research
184+ open-access research outputs.
In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.…
Terminal airspace congestion remains a major bottleneck in the global air traffic network. Although the Aircraft Sequencing and Scheduling Problem (ASSP) has been widely studied, many methods rely on …
If a finite group $G$ acts on a rational homology manifold, then the orbit space is well-known to be a rational homology manifold again. We consider here actions on spaces that may be much more singul…
The Alon-Tarsi number of a graph $ G $ is the smallest $ k $ such that there exists an orientation $ D $ of $ G $ with maximum outdegree $ k - 1 $ satisfying that the number of even Eulerian subgraphs…
Many open problems in combinatorics admit reformulations in which a global construction can be achieved by the repeated application of small, finite correcting steps. This paper presents three computa…
In this article, we first introduce the one-sided BLO space $\mathrm{BLO}^+(\mathbb{R})$ and characterize it, respectively, in terms of the one-sided Muckenhoupt class $A_1^+(\mathbb{R})$ and the one-…
We prove that a complete Riemannian manifold with a positive uniform lower bound on injectivity radius and a positive uniform lower bound on Ricci curvature admits an $L^\infty$-close (bi-Lipschitz) s…
Grid diagrams are special representations of knots in the three-sphere that are used to define a combinatorial version of knot Floer homology. Paolo Ghiggini and Yi Ni showed that knot Floer homology …
This article compares different proving methods for projective incidence theorems. In particular, a technique using quadrilateral tilings recently introduced by Sergey Fomin and Pavlo Pylyavskyy is sh…
There are multiple generalisations of the Pythagorean theorem to spherical and hyperbolic geometry. A natural one, involving areas of disks with radii equal to the sides of a proper triangle, was disc…
Assume $G$ is a graph, $(v_1,\ldots,v_k)$ is a sequence of distinct vertices of $G$, and $(a_1,\ldots,a_k)$ is an integer sequence with $a_i \in \{1,2\}$. We say $G$ is \emph{$(a_1,\ldots,a_k)$-list e…
We study two measures of uncolourability of cubic graphs, their colouring defect and perfect matching index. The colouring defect of a cubic graph $G$ is the smallest number of edges left uncovered by…
The \emph{Alon-Tarsi number} of a graph $G$ is the smallest $k$ so that there exists an orientation $D$ of $G$ with max outdegree $k-1$ satisfying the number of even Eulerian subgraphs different from …
Cai et al.\ proved that a toroidal graph $G$ without $6$-cycles is $5$-choosable, and proposed the conjecture that $\textsf{ch}(G) = 5$ if and only if $G$ contains a $K_{5}$ [J. Graph Theory 65 (2010)…
For an arbitrary hypersurface singularity, we construct a family of semigroups associated with algebraically closed fields that arise as an infinite union of rings of series. These semigroups extend t…
Given a hypergraph $H=(V,E)$, define for every edge $e\in E$ a linear expression with arguments corresponding with the vertices. Next, let the polynomial $p_H$ be the product of such linear expression…
Assume $G$ is a bridgeless graph. A cycle cover of $G$ is a collection of cycles of $G$ such that each edge of $G$ is contained in at least one of the cycles. The length of a cycle cover of $G$ is the…
These are notes of my lecture courses given in the summer of 2024 in the School on Number Theory and Physics at ICTP in Trieste and in the 27th Brazilian Algebra Meeting at IME-USP in S\~ao Paulo. We …
This article is concerned with the Axiom of Choice (AC) and the well-ordering theorem (WO) in second-order predicate logic with Henkin interpretation (HPL). We consider a principle of choice introduce…
This article is concerned with the Axiom of Choice (AC) and the well-ordering theorem (WO) in second-order predicate logic with Henkin interpretation (HPL). We consider a principle of choice introduce…
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