3 stories tagged with #combinatorics, in publish-time order across the WeSearch catalog. Tag pages update as new stories ingest.
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ARXIV.ORG
Humans have disproved the sum-product conjectures for real numbers
We disprove the sum-product conjecture for real numbers by constructing arbitrarily large $A\subset \mathbb{R}$ (whose elements are algebraic integers in a number field of degree $…
ARXIV CS.AI
Solving Combinatorial Counting Problems with Weighted First-Order Model Counting
Combinatorial counting problems pervade artificial intelligence, statistics, and discrete mathematics. Whether the task is enumerating subsets, multisets, permutations, partitions,…
ARXIV.ORG
An explicit lower bound for the unit distance problem
We show that there are sets of $n$ points in the plane with $n$ arbitrarily large that contain more than $n^{1.014}$ pairs of points separated by a distance exactly $1$. This impro…