External difference families (EDFs) are combinatorial objects which were introduced in the early 2000s, motivated by information security applications such as the construction of AMD codes. Various generalizations have since been defined and investig...
We derive the rational generating function that enumerates the angels and devils in M. C. Escher's {\it Circle Limit IV} according to their combinatorial distance from the six creatures whose feet meet at the center of the disk. This result shows tha...
We explore the concept of real tropical basis of an ideal in the field of real Puiseux series. We show explicit tropical bases of zero-dimensional real radical ideals, linear ideals and hypersurfaces coming from combinatorial patchworking. But we als...
We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orders which we call pseudo-pr...
We discuss some seemingly unrelated observations on integers, whose close or farther away neighbors show a complex of combinatorial, ordering, arithmetical or probabilistic properties, emphasizing puzzlement in more common expectations....
Vehicle Routing Problem is a well-known problem in logistics and transportation, and the variety of such problems is explained by the fact that it occurs in many real-life situations. It is an NP-hard combinatorial optimization problem and finding an...
Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a combinatorial explosion in the complex size. For $n$ points in $\mathbb{...
Fix a finite set of points in Euclidean $n$-space $\euc^n$, thought of as a point-cloud sampling of a certain domain $D\subset\euc^n$. The Rips complex is a combinatorial simplicial complex based on proximity of neighbors that serves as an easily-c...
Following the work of Altmann and Hausen we give a combinatorial description in terms for smooth Fano threefolds admitting a 2-torus action. We show that a whole variety of properties and invariants can be read off from this description. As an applic...
Trades are important objects in combinatorial design theory that may be realized as certain elements of kernels of inclusion matrices. Total trades were introduced recently by Ghorbani, Kamali and Khosravshahi, who showed that over a field of charact...
We propose a combinatorial game on finite graphs, called Salmagundy, that is played by two protagonists, Dido and Mephisto. The game captures the logical structure of a proof of the resolution of singularities. In each round, the graph of the game is...
Stanley (1986) showed how a finite partially ordered set gives rise to two polytopes, called the order polytope and chain polytope, which have the same Ehrhart polynomial despite being quite different combinatorially. We generalize his result to a wi...
The Necklace Splitting problem is a classical problem in combinatorics that has been intensively studied both from a combinatorial and a computational point of view. It is well-known that the Necklace Splitting problem reduces to the discrete Ham San...
Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and multimodal parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial lib...
6 days ago · combinatorics number-theory integers additive-combinatorics combinatorial-designs Cite edited yesterday asked Feb 27 at 21:06
Occam's Razor tells us to pick the simplest model that fits our observations. In order to make sense of his process mathematically, we interpret it in the context of posets of functions. Our approach leads to some unusual new combinatorial problems c...
This paper studies how a domain-independent planner and combinatorial search can be employed to play Angry Birds, a well established AI challenge problem. To model the game, we use PDDL+, a planning language for mixed discrete/continuous domains that...
[NeurIPS 2023] T2T: From Distribution Learning in Training to Gradient Search in Testing for Combinatorial Optimization (⭐ 71)
We introduce and develop the theory of UMEL-shellable posets. These are posets equipped with an edge-lexicographical labeling satisfying certain uniformity and monotonicity properties. This framework encompasses classical families of combinatorial ge...
We use higher parallel transport -- more precisely, the integration A_{infty}-functor constructed by Block-Smith and Arias Abad-Schaetz -- to define Reidemeister torsion for flat superconnections. We hope that the combinatorial Reidemeister torsion c...