Machina Mathematica

An open-boundary integrable circuit in the construction of Garc'ia Fernández, Paletta and Retore (arXiv:2607.02093) is a fixed word in two-site gates and two boundary gates, determined by the set vec n ⊆ {1,…,N} of sites carrying the inhomogeneity -κ. They…

Guo, Yang and Zagier (arXiv:2603.15233) normalise Witten's psi-class intersection numbers as C(d)=2²ᵍ∏ⱼ(2dⱼ+1)!! / (3²ᵍ⁻²⁺ⁿ(2g-3+n)!)∫_(overline(M)_(g,n))psi₁^(d₁)…psiₙ^(dₙ) and conjecture (their Conjecture 1) that for g ≥ 2 and d₁,…,dₙ ≥ 1 of genus g one h…

A weighing design W(m, z)k in the sense of Lejeune Herman and Goos (arXiv:2608.04814) is an m × z matrix over {0, ± 1} with exactly k non-zero entries in every column, at most m-k zeros in every row, and W^(T)W=kI_z. Their Table 1 counts the isomorphism cla…

The center of distances of a metric space (X,d) is the set C(X) of those distances t for which the equation d(p,x)=t has a solution x for every p ∈ X. Dovgoshey and Rovenska (arXiv:2601.13363, Mathematics 2026) described C(X) for ultrametric spaces generate…

Chau and Shah (arXiv:2603.28487) call a finite simple graph G TB-symmetrical when, for every two cycle lengths r ≠ s, the numbers of r-cycles through each edge, through each pair of adjacent edges and—with a sign recording orientation—through each pair of n…

Cavalagli, Bemporad and Zanon (IEEE Control Systems Letters textbf(10) (2026), 919–924) bound the number of hyperbolic feedback Nash equilibria of the symmetric N-player scalar discounted linear-quadratic game xₜ₊₁=axₜ+Σᵢ u_(i,t) and show that the maximal n…

A rank-metric code C ⊆ 𝔽_(qᵐ)ⁿ is rank-metric intersecting when the rank supports of any two nonzero codewords meet nontrivially (Bartoli, Borello, Marino and Scotti, arXiv:2507.00569); a nondegenerate [n,k,d]_(qᵐ/q) code has this property if and only if i…

Leuenberger and Albrizzio (arXiv:2606.21425) show that the weight spectrum of the Reed–Muller code RM(7,14) contains every even integer between 312 and 2¹⁴-312, together with the classical small and large weights, with the possible exception of a set M of t…

In the assignment (house allocation) domain of n agents, n houses and strict preferences, an assignment μ majority dominates λ when more agents prefer their house under μ than under λ; because this relation has ties, there are three covering relations — Bor…

To a prime p and a subgroup E ≤ ℤₚ^(×) containing -1, Marashdeh attaches a nested chain of subspaces V₀ ⊆ V₁ ⊆ … of ℂᵖ, generated from the two point masses δ₀,δ₁ by the class matrices of the cyclotomic scheme and the diagonal idempotents of the basepoint pa…

Herings, Seel and Predtetchinski (arXiv:2606.23440) consider n individuals whose utilities for the networks on them are independent atomless random variables, and the number sₙ of pairwise stable networks in the sense of Jackson and Wolinsky. They prove E(s…

For λ>-1/2 rational and ζ a nonzero zero of the Bessel function J_(λ-1), the monic orthogonal polynomials for the weight (1-x²)^(λ-1/2)e^(iζ x) on [-1,1] satisfy xPₙ=Pₙ₊₁+iαₙPₙ+βₙPₙ₋₁. Lyu and Zhou (arXiv:2607.19797) derive a first-order coupled system of d…

A decision-maker who will observe n i.i.d. binary signals of unknown precision π ∈ [1/2,1] commits in advance to a belief aₖ for every count k of high signals; an adversarial Nature mixes over π; the payoff is the mean-squared-error regret against an oracle…

Meghaichi and Xing (arXiv:2606.12632) discretise nonlinear conservation laws with uncertainty by replacing the multiplication on the space P_K of polynomials of degree at most K in the random variable by an associative truncated product (ATP), and they tabu…

Let Tm(m)(B) = I + B + … + Bᵐ⁻¹ be the radix-m kernel of the truncated Neumann series and let μₘ be the least number of matrix products with which a straight-line program (products of linear combinations, starting from I and B; additions and scalings free)…

Let πₙᶜⁱʳᶜ be the real polynomials of degree at most n bounded by 1 on [-1,1] and Tₙ the Chebyshev polynomial. Bojanov's problem, as recorded by Naidenov, asks whether ∫₋₁¹φ(|P^((k))|)<∫₋₁¹φ(|Tₙ^((k))|) for every strictly increasing convex φ, every P ∈ πₙᶜⁱ…