Tag: Upper and lower bounds
Entropy bounds limit perfect matchings in bipartite hypergraphs
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in MathematicsWhat the study found The authors prove an upper bound on the number of A-perfect matchings in uniform bipartite hypergraphs with small maximum codegree. They also derive bounds for related counting problems in Latin squares and regular hypergraphs. Why the authors say this matters The study suggests that these bounds help quantify how many perfect…
Upper bounds improve for residual finiteness growth in two-step nilpotent groups
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in MathematicsWhat the study found The authors report an improved polylogarithmic upper bound for the residual finiteness growth of two-step nilpotent groups. They also state that this bound depends only on the group’s complex Mal’cev completion, and that it is exact when the commutator subgroup is one- or two-dimensional. Why the authors say this matters The…
Bootstrap bounds constrain supersymmetric quantum mechanics
What the study found The study found that the quantum-mechanics bootstrap can be applied to supersymmetric quantum mechanics (SUSY QM) and to the Marinari-Parisi matrix model, producing rigorous bounds on ground-state data. In cases where supersymmetry is spontaneously broken, the bounds apply to the lowest-energy normalizable eigenstate. Why the authors say this matters The authors…
Minimal partitions can exist in unbounded domains
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in MathematicsWhat the study found The study finds that for unbounded domains, including domains of infinite volume, spectral minimal partitions can exist below a threshold determined by the essential spectrum and the best “k-1” partition energy. The behavior at the threshold differs by the choice of p: for p < ∞, minimizing partitions may or may…
Edge version of graph inducibility is determined by fractional independence number
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in MathematicsWhat the study found The study shows that the edge version of inducibility for any graph H satisfies ρ(H,m) = Θ(m^α_f(H)), where α_f(H) is the fractional independence number of H. The authors also give additional bounds and conjectures for paths and cycles. Why the authors say this matters The authors indicate that this result shifts…
Dark decay channels strengthen cosmological bounds on heavy neutral leptons
Cosmological analysis shows heavy neutral leptons with dark decay modes face stronger big bang nucleosynthesis constraints, not weaker ones, narrowing viable parameter space for terrestrial detection.
