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 2
Rank-metric intersecting codes
Intersecting codes are codes in which any two nonzero codewords share a common nonzero coordinate, and they have been extensively studied due to their applications in communication theory…Path Decompositions of Sparse Graphs via Gaussian Sweeps and Faster Exponential Algorithms
Using the bisection bound of Monien and Preis, Fomin and Høie proved in 2006 that every graph of maximum degree 3 on $n$ vertices has pathwidth at most $n/6+o(n)$.Beyond the Bochner Method: Optimal Spectral Gaps for Block Dynamics of Spin Systems like the $O(N)$ Model
Let $μ$ be a probability distribution on a spin system with $n$ sites and possibly infinite spin spaces.On the most informative Boolean function under noise
Let $X$ be a uniform random bit string and $Y$ be obtained by flipping each bit of $X$ independently with probability $p$.Stabiliser codes over prime fields as weighted graphs and as quantum sets of lines
We further develop the theory of quantum stabiliser codes and its links with graph theory and finite geometry.Quantum error correcting codes from quiver moduli: Grassmannians, cyclic monodromy, and argyle collision divisors
Building on aspects of a recent diagrammatic field-theory programme for quantum error correction put forward by the first-named author (arXiv:2607.08911), we construct exact finite-dimensional codes…Large independent sets via neighborhood block dynamics, Glauber dynamics, and local occupancy
Local occupancy can be used to bound the expected size of a hard-core independent set.Full-Rank Constructions of Explicit Lossless Expanders and Good Small-Set qLTCs
We construct explicit two-sided lossless expanders whose binary adjacency matrices have full rank, and use them to obtain explicit asymptotically good quantum LDPC codes whose specified X- and…Reed-Muller Codes are Optimal Binary Linear 3-Query LCCs
We prove that any linear $3$-query locally correctable code $C \colon \mathbb{F}_2^k \to \mathbb{F}_2^n$ with constant correction radius must have length $n \geq 2^{Ω(\sqrt{k})}$.Asymptotically Optimal Weighted Edge Colorings via Local Bin Packing
We study weighted edge coloring, where each edge of a graph $G$ has a weight in $(0,1]$, and colors are assigned so that the incident weight of each color at every vertex is at most one.The Optimizer's Windfall: Bounding Hindsight Gain under Random Restrictions
Suppose an optimization problem is randomly restricted, independently on each variable, and re-optimized after the restriction is revealed.Uniform Sampling of Linear Codes with Prescribed Hull Dimension
We give exactly uniform samplers for linear codes with prescribed hull dimension, for the Euclidean, Hermitian, and symplectic inner products and over finite fields of every characteristic.Get Permanent Results Faster by Counting Stars
We show that $n \times n$ permanents can be computed with $O^*{(2-\varepsilon)^n}$ arithmetic operations over every commutative ring, for $\varepsilon = 10^{-40}$.A King for Almost Everyone
A tournament is an orientation of a complete graph.An $\mathsf{FPRAS}$ for Mixed Volumes
We design the first fully polynomial-time randomized approximation scheme ($\mathsf{FPRAS}$) to estimate the mixed volume of $n$ arbitrary compact convex sets in $\mathbb{R}^{n}$ specified by weak…Approximation Algorithms for Maximum-Weight Degree-Bounded Forests
In the maximum-weight degree-bounded forest problem, we are given a graph with nonnegative edge weights and a degree upper bound on each vertex.Improved lower bounds for the kissing number in dimensions 49 to 61
We give explicit kissing configurations in R^d for every d = 49, ..., 61.Limits and Constants of OpenAI's Claimed ETH Refutation
A recent OpenAI preprint claims a deterministic algorithm that counts the satisfying assignments of a $k$-CNF formula in time $2^{O_k(n\log\log n/\sqrt{\log n})}$, and $2^{O(n/\sqrt{\log n})}$ at…The covering radius of the first-order Reed-Muller code in nine variables is 242
We prove that the covering radius of the binary first-order Reed-Muller code RM(1,9) is exactly 242.A density theorem for non-standard irreducible cyclic codes
We prove a fixed-characteristic density form of the Berger-Charpin conjecture for non-degenerate irreducible cyclic codes: for each prime $p$, the lengths admitting such a non-standard code over…