We study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals. While the packing problem is currently unresolved, we successfully settle the validity of i...
The Multiple Depot Ring-Star Problem (MDRSP) is an important combinatorial optimization problem that arises in the context of optical fiber network design, and in applications pertaining to collecting data using stationary sensing devices and autonom...
The notion of stationary reflection is one of the most important notions of combinatorial set theory. We investigate weak reflection, which is, as the name suggests, a weak version of stationary reflection. This sort of reflection was introduced in...
We study the robustness of deep reinforcement learning algorithms against distribution shifts within contextual multi-stage stochastic combinatorial optimization problems from the operations research domain. In this context, risk-sensitive algorithms...
Let $\mathbf{H}$ be the Cartesian product of a family of finite abelian groups. Via a polynomial approach, we give sufficient conditions for a partition of $\mathbf{H}$ induced by weighted poset metric to be reflexive, which also become necessary for...
Jun 26, 2017 · Always use blocking assignments for combinatorial or level-sensitive code, as well a clock assignments Always use non-blocking assignments for variables that are written on a clock …
Jun 26, 2017 · Always use blocking assignments for combinatorial or level-sensitive code, as well a clock assignments Always use non-blocking assignments for variables that are written on a clock …
Jun 3, 2025 · The Technology Convergence Report 2025 offers leaders a strategic lens – the 3C Framework – to help them navigate the combinatorial innovation era.
Jun 3, 2025 · The Technology Convergence Report 2025 offers leaders a strategic lens – the 3C Framework – to help them navigate the combinatorial innovation era.
Jun 3, 2025 · The Technology Convergence Report 2025 offers leaders a strategic lens – the 3C Framework – to help them navigate the combinatorial innovation era.
element of chance; solving such a game may use combinatorial game theory or computer assistance. A two-player game can be solved on several levels: Prove
always force either a victory or a draw (see solved game). It is also related to more generally solving chess-like games (i.e. combinatorial games of
The purpose of the article is to provide partial proofs for two conjectures given by Witte and Forrester in "Moments of the Gaussian $β$ Ensembles and the large $N$ expansion of the densities" with the use of the topological recursion adapted for ge...
W. Thurston proved that to a triangulation of the sphere of non-negative combinatorial curvature, one can associate an element in a certain lattice over the Eisenstein integers such that its orbit is a complete invariant of the triangulation. In th...
We prove several combinatorial properties of suffix arrays, including a characterization of suffix arrays through a bijection with a certain well-defined class of permutations. Our approach is based on the characterization of Burrows-Wheeler arrays g...
Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize 2-dimensional CAT(0) cube complexes and are a square analog of systolic complexes. We introduce and study the basic...
The activities and interactions of proteins that govern the cellular response to a signal generate a multitude of protein phosphorylation states and heterogeneous protein complexes. Here, using a computational model that accounts for 307 molecular...
This paper explores the structure of the combinatorial domain $2^X$ in relation to sunflowers. The previous study found some intrinsic properties of the $l$-extension \[ Ext \left( \mathcal{F}, l \right) = \left\{ V ~:~ V \in {X \choose l},~ \exists...
We introduce new objects, the interval-posets, that encode intervals of the Tamari lattice. We then find a combinatorial interpretation of the bilinear form that appears in the functional equation of Tamari intervals described by Chapoton. Thus, we r...
Can AI based methods help us make advances in complexity theory? We provide evidence towards answering this in the affirmative, using AlphaEvolve (an LLM code mutation agent) to obtain new results in three settings: a) We improve a recent result of...