PAFP is FPT by BFS-width plus backward arcs in the union digraph and polynomial-time solvable via 2-SAT for DAGs of exact-length width 2, with matching NP-hardness for width 3.
Journal of Algorithms12(2), 308–340 (1991)
5 Pith papers cite this work. Polarity classification is still indexing.
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Matroids satisfy a generalized basis exchange where for X and Y in the symmetric difference of bases A and B there exist U and V containing them with |U|=|V| at most rank(X+Y) such that A-U+V and B+U-V are bases, plus a framework for Grassmann-Plücker extensions in characteristic-zero representable
Partition ranks bound multiplicative complexity from below for constant-degree multilinear arithmetic circuits, generalizing Strassen's tensor-rank characterization.
A neuron-astrocyte network with dual-timescale memory reduces median path lengths up to sixfold in partially observable grid-world navigation tasks.
Derives a second-order sum rule for eigenvalues of abstract Hamiltonian families and applies it to Lieb-Thirring bounds, Bessel zeros, and trace inequalities.
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Sum rules and a second order Feynman-Hellman theorem for abstract operators with applications
Derives a second-order sum rule for eigenvalues of abstract Hamiltonian families and applies it to Lieb-Thirring bounds, Bessel zeros, and trace inequalities.