We introduce and study the Marco Polo problem, which is a combinatorial approach to geometric localization. In this problem, we are told there are one or more points of interest (POIs) within distance $n$ of the origin that we wish to localize. Given...
Branch-and-bound is a typical way to solve combinatorial optimization problems. This paper proposes a graph pointer network model for learning the variable selection policy in the branch-and-bound. We extract the graph features, global features and h...
We present new combinatorial objects, which we call grid-labelled graphs, and show how these can be used to represent the quantum states arising in a scenario which we refer to as the faulty emitter scenario: we have a machine designed to emit a part...
The main challenge of combinatorial game theory is to handle combinatorial chaos, if one player knows the strategy better than his opponent, he is able to determine the exact results of a game. If both players are qualified competitor, the result usu...
We study $T$-designs in the nonbinary Johnson scheme. This scheme generalizes both the Johnson and Hamming schemes and admits a bivariate $Q$-polynomial structure. Zhu (2021) provided a combinatorial characterization of $T$-designs in this scheme for...
Diffusion models have recently advanced Combinatorial Optimization (CO) as a powerful backbone for neural solvers. However, their iterative sampling process requiring denoising across multiple noise levels incurs substantial overhead. We propose to l...
Combinatorial Testing (CT) tools are essential to test properly a wide range of systems (train systems, Graphical User Interfaces (GUIs), autonomous driving systems, etc). While there is an active research community working on developing CT tools, pa...
We study the stochastic combinatorial semi-bandit problem with unrestricted feedback delays under merit-based fairness constraints. This is motivated by applications such as crowdsourcing, and online advertising, where immediate feedback is not immed...
Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics. "Combinatorial Physics is an emerging area
We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show that the...
We research a combinatorial game based on the Cookie Monster problem called the Cookie Monster game that generalizes the games of Nim and Wythoff. We also propose several combinatorial games that are in between the Cookie Monster game and Nim. We dis...
In this paper we construct families of bit sequences using combinatorial methods. Each sequence is derived by con- verting a collection of numbers encoding certain combinatorial nu- merics from objects exhibiting symmetry in various dimensions. Using...
We introduce a class of $f(t)$-factorials, or $f(t)$-Pochhammer symbols, that includes many, if not most, well-known factorial and multiple factorial function variants as special cases. We consider the combinatorial properties of the corresponding ge...
We study online combinatorial allocation problems in the secretary setting, under interdependent values. In the interdependent model, introduced by Milgrom and Weber (1982), each agent possesses a private signal that captures her information about an...
Set-valued tableaux play an important role in combinatorial $K$-theory. Separately, semistandard skyline fillings are a combinatorial model for Demazure atoms and key polynomials. We unify these two concepts by defining a set-valued extension of semi...
We introduce the notion of an arithmetical type of combinatorial family of reals, which serves to generalize different types of families such as mad families, maximal cofinitary groups, ultrafilter bases, splitting families and other similar types of...
We define a "combinatorial Hopf algebra" as a Hopf algebra which is free (or cofree) and equipped with a given isomorphism to the free algebra over the indecomposables (resp. the cofree coalgebra over the primitives). The choice of such an isomorph...
In discrete calculus it's the poset $\mathbb {Z}_ {\ge 0}$ under the usual order. This beautiful theory was first described by Gian-Carlo Rota in On the Foundations of Combinatorial Theory I, and elaborated …
Combinatorial game theory (abbreviated CGT) is the subfield of combinatorics (not traditional game theory) which deals with games of perfect information such as Nim and Go. It includes topics such as …
Jul 22, 2016 · Moreover, a simple combinatorial [fixed point or not fixed point]-argument (see next section) can be used to alternatively confirm $\text { (1)}$ by counting permutations,