Applied Math · Mathematics & Statistics
Combinatorics
The newest papers in Combinatorics that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
228 papers, from 31 August 2026 to 5 November 2026: 168 arXiv preprints and 60 OpenAlex records.
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Newest papers, page 8
Grid Theory and Polynomiality in Dynamic Lot-Sizing
Why are some dynamic lot-sizing problems polynomial?Resolving Erdős-Ulam Monochromatic Union-Closed Family Conjectures
We prove both Erdős-Ulam conjectures on monochromatic union-closed families.Optimal large sieve for fixed order characters
Let $n \geq 3$.Coloring 3-colorable graphs with $O(n^{4/23})$ colors via a Gaussian-cover recursion
We give a randomized polynomial-time algorithm that colors any promised $3$-colorable graph on $n$ vertices with $\smash{O(n^{4/23}) = O(n^{0.17391\ldots})}$ colors, improving on the recent bounds…Stable and Online Algorithms for Random Matrix Discrepancy
We study the average-case matrix discrepancy problem: given independent normalized $d\times d$ Gaussian orthogonal ensemble matrices $A_1,\dots,A_N$ and a fixed margin $κ>0$, find signs…The isoperimetric problem for four-dimensional parallelohedra
The honeycomb and Kelvin problems ask how space can be partitioned into cells of equal volume with the least surface area.Beyond Liu's 0.382709 threshold for the union-closed sets conjecture
The union-closed sets conjecture asks whether every finite union-closed family containing a nonempty set has an element contained in at least half of its members.MultiTable: A Faster Hash Table at any Physical Load Factor up to and Including One
We present \emph{multitable} and its Rust reference implementation: a stable hash table both materially faster at equal physical memory and more flexible than the SwissTable in its Rust's hashbrown…Quantum State Routing and Perfect State Transfer on Signed Graphs under Environmental Noise
Routing unknown quantum information across distributed communication networks requires autonomous, measurement-free mechanisms to prevent wave-function collapse.Submodularity of entropy under quantum convolution
We develop a submodular framework for the von Neumann entropy of discrete quantum convolutions, providing a noncommutative counterpart to the direct side of entropic additive combinatorics.The Reach of Abelian Covers in Hypergraphs
Covers in hypergraphs are frequently studied to capture various forms of dependence between hyperedges.There is no $8$-regular $K_3$-irregular graph
A graph is $K_3$-irregular if its vertices belong to pairwise distinct numbers of triangles.The directed temporal exploration problem
We study the temporal exploration problem on temporal digraphs.A polylogarithmic higher-order Cheeger inequality
Let $λ_k(G)$ be the $k$th eigenvalue of the normalized Laplacian of a finite undirected weighted graph, and let $ρ_G(k)$ be the minimum possible maximum conductance of $k$ disjoint nonempty vertex…Large-Scale Autonomous Discovery of Kissing Number Constructions
The kissing-number problem is a classical problem in discrete geometry whose exact solution is known in only a few dimensions.Fast factorization in diagram monoids
We give explicit algorithms that factor elements of the standard diagram monoids into their usual generators.Odd Cycle Transversal on $H$-free graphs
\textsc{Odd Cycle Transversal} is a classic $\mathsf{NP}$-hard graph optimization problem asking for a minimum-weight set of vertices whose deletion makes the input graph bipartite, or equivalently…The Tight Upper Bound on the Number of Distinct Squares in Circular Words
A square is a word $xx$, where $x$ is nonempty.Further Results on Sum-Freedom of Binary and $q$-ary Functions
The notion of sum-freedom of binary functions was introduced recently by C. Carlet as a generalization of the APN functions used in cryptography; the $q$-ary version of the notion is a natural…Boolean threshold functions, neuron capacity, and memory retrieval
How much information can a single neuron remember?