In number theory, the larger sieve is a sieve invented by Patrick X. Gallagher. The name denotes a heightening of the large sieve. Combinatorial sieves
We show in this article how Girard Desargues, in his well known text on conics, the \textit{Brouillon Project,} manages to use Menelaos' theorem with some awesome virtuosity. To this end, we propose a detailed analysis of his \textit{combinatorial} a...
The Thief Orienteering Problem (ThOP) is a multi-component problem that combines features of two classic combinatorial optimization problems: Orienteering Problem and Knapsack Problem. The ThOP is challenging due to the given time constraint and the...
We tackle the Thief Orienteering Problem (ThOP), an academic multi-component problem that combines two classical combinatorial problems, namely the Knapsack Problem and the Orienteering Problem. In the ThOP, a thief has a time limit to steal items th...
We investigate the combinatorial interplay between automorphisms and opposition in (primarily finite) generalised polygons. We provide restrictions on the fixed element structures of automorphisms of a generalised polygon mapping no chamber to an opp...
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph method, are theo...
The famous combinatorial problem of Euler concerns an arrangement of $36$ officers from six different regiments in a $6 \times 6$ square array. Each regiment consists of six officers each belonging to one of six ranks. The problem, originating from S...
Based on results by Brugallé and Mikhalkin, Fomin and Mikhalkin give formulas for computing classical Severi degrees $N^{d, δ}$ using long-edge graphs. In 2012, Block, Colley and Kennedy considered the logarithmic version of a special function asso...
A central challenge in quantum machine learning is the design and training of parameterized quantum circuits (PQCs). Much like in deep learning, vanishing gradients pose significant obstacles to the trainability of PQCs, arising from various sources....
Offline reinforcement learning in high-dimensional, discrete action spaces is challenging due to the exponential scaling of the joint action space with the number of sub-actions and the complexity of modeling sub-action dependencies. Existing methods...
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered too weak t...
In 2002, Andrews, Lewis, and Lovejoy introduced the combinatorial objects which they called partitions with designated summands. These are constructed by taking unrestricted integer partitions and designating exactly one of each occurrence of a part....
Fukaya categories are deep and rich invariants of symplectic manifolds which are notoriously difficult to compute explicitly. In the case of surfaces, however, the situation is simple, combinatorial,and is very well understood (at least by experts)....
We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different way...
A. Bak developed a combinatorial approach to higher $K$-theory, in which control is kept of the elementary operations involved, through paths and `paths of paths' in what he called a global action. The homotopy theory of these was developed by G. M...
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles introduction t...
In an all-pay auction, only one bidder wins but all bidders must pay the auctioneer. All-pay bidding games arise from attaching a similar bidding structure to traditional combinatorial games to determine which player moves next. In contrast to the es...
We introduce a novel approach to solving dynamic programming problems, such as those in many economic models, on a quantum annealer, a specialized device that performs combinatorial optimization. Quantum annealers attempt to solve an NP-hard problem...
Tatsuyuki Hikita recently proved the Stanley--Stembridge conjecture using probabilistic methods, showing that the chromatic symmetric functions of unit interval graphs are $e$-positive. Finding a combinatorial interpretation for these $e$-coefficient...
In this research note, we lay some groundwork for analyzing the manipulability of core-selecting payment rules in combinatorial auctions. In particular, we focus on payment rules based on the bidders' Shapley values. We define a sensitivity metric, a...