For linear-rate master equations the generating function admits an exact composition-multiplier representation whose Taylor coefficients on any finite window are obtained from a closed lower-triangular ODE of size 2(N+1), independent of the truncation cap N; the same closure is combined with Strang–
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Saddle-point asymptotics for chromatic and Tutte polynomials of complete multipartite graphs prove Kotesovec's fixed-column conjecture and yield fixed-part and all-order expansions for OEIS sequences.
Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order perturbative contributions.
Pin classes exhibit a phase transition at μ ≈ 3.28277 with countably many below the threshold and uncountably many at it; all growth rates below μ are classified via periodic pin permutations.
A genus-preserving chord swap Markov chain on chord diagrams is shown to mix in polynomial time for any fixed genus.
Algebraic characterization of runtime pgfs for GCP programs via kernel polynomial roots yields dominant singularities and exact asymptotics for single-state cases.
Implicit formula for critical curve α_c(κ) of loop percolation on d-regular trees, positive for κ>κ_c=2√(d-1)/d-1, with mean-field exponents for κ>κ_c and quadratic percolation probability at κ=κ_c.
Derives closed-form critical parameters, equation of state, binodal and spinodal curves for the cell fluid model in the J2 ≫ J1 limit matching van der Waals lattice gas, plus analytical extension to marginal J1=J2 stability using deformed exponential asymptotics.
Local goal support in policy functional graphs predicts goal failure in sparse GCRL with F1 0.925, and a taxonomy explains residual failures from competing attractors.
The mixed Hessian develops exactly one logarithmically diverging eigenvalue per symmetry block at the analytic threshold zeta_c, with the remaining spectrum bounded, and scalar Gram functions continue regularly past the geometric threshold.
Uniform random d-regular bipartite planar maps converge locally to an almost surely one-ended recurrent infinite map.
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Saddle-Point Asymptotics for Chromatic and Tutte Polynomial Evaluations of Complete Multipartite Graphs
Saddle-point asymptotics for chromatic and Tutte polynomials of complete multipartite graphs prove Kotesovec's fixed-column conjecture and yield fixed-part and all-order expansions for OEIS sequences.