In this paper, we study tree--like tableaux and some of their probabilistic properties. Tree--like tableaux are in bijection with other combinatorial structures, including permutation tableaux, and have a connection to the partially asymmetric simple...
In light of the COVID-19 pandemic, it is an open challenge and critical practical problem to find a optimal way to dynamically prescribe the best policies that balance both the governmental resources and epidemic control in different countries and re...
If you want to fill $n \in \mathbb{N}$ seats in succession with $n$ people and the rule that each person chooses one of the seats with the maximum distance to an occupied seat, then you can ask yourself how many possibilities there are for this. In t...
Autonomous agents and systems cover a number of application areas, from robotics and digital assistants to combinatorial optimization, all sharing common, unresolved research challenges. It is not sufficient for agents to merely solve a given task; t...
We provide answers to natural combinatorial questions which arise from learning the rules to Tak. We solve the discarded cases of the $3\times 3$ game not previously considered by Joshua Achiam, showing that Player $1$ has a forced win from any start...
Nim is a well-known combinatorial game with several variants, e.g., Delete Nim and Variant Delete Nim. In Variant Delete Nim, the player deletes one of the two heaps of stones and splits the other heap on his/her turn. In this paper, we discuss gener...
In this paper, we analyze the misère versions of two impartial combinatorial games: k-Bounded Greedy Nim and Greedy Nim. We present a complete solution to both games by showing necessary and sufficient conditions for a position to be P-positions....
The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: build...
This paper introduces a variant of the impartial combinatorial game nim, called tree nim, as well as a particular case of tree nim called tripod nim. A certain existence-uniqueness result and a periodicity result are proven about the distribution of...
We obtain lower bounds on the rank of the kappa ring of the Delign-Mumford compactification of the moduli space of curves in different degrees. For this purpose, we introduce a quotient of the kappa ring, the combinatorial kappa ring, and show that t...
We give a simple combinatorial criterion allowing to recognize whether a string (or, more generally, a special biserial) algebra is a laura algebra or not. We also show that a special biserial algebra is laura if and only if it has a finite number...
Jun 3, 2025 · The Technology Convergence Report 2025 offers leaders a strategic lens – the 3C Framework – to help them navigate the combinatorial innovation era.
Two line arrangements in $\mathbb{CP}^2$ can have different topological properties even if they are combinatorially isomorphic. Results by Dan Cohen and Suciu and by Randell show that a reducible moduli space under complex conjugation is a necessary...
We prove some necessary conditions for a link to be either concordant to a quasi-positive link, quasi-positive, positive, or the closure of a positive braid. The main applications of our results are a characterisation of positive links with unlinking...
J.M. Tomczak, ”Deep Generative Modeling”, Springer, Cham, 2022 (The first comprehensive book on Generative AI) CY. Oh, J.M. Tomczak, E. Gavves, M. Welling, Combinatorial Bayesian Optimization …
Goodwillie's calculus of homotopy functors associates a tower of polynomial approximations, the Taylor tower, to a functor of topological spaces over a fixed space. We define a new tower, the varying center tower, for functors of categories with a fi...
Chip-firing is a combinatorial game played on an undirected graph in which we place chips on vertices. We study chip-firing on an infinite binary tree in which we add a self-loop to the root to ensure each vertex has degree 3. A vertex can fire if th...
Using a recently proposed model for combinatorial landscapes, Local Optima Networks (LON), we conduct a thorough analysis of two types of instances of the Quadratic Assignment Problem (QAP). This network model is a reduction of the landscape in which...
Local Optima Networks (LONs) have been recently proposed as an alternative model of combinatorial fitness landscapes. The model compresses the information given by the whole search space into a smaller mathematical object that is the graph having as...
The Divide and Distribute Fixed Weights algorithm (ddfw) is a dynamic local search SAT-solving algorithm that transfers weight from satisfied to falsified clauses in local minima. ddfw is remarkably effective on several hard combinatorial instances....