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Brenti Problem 2.6: does the τ-polynomial τ(G;x) have only real roots for every graph G?

Status: Open.

#406 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 21, 2026

Compound (exterior-power) matrices: multiplicativity and eigenvalue products

Status: Open.

#405 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 21, 2026

Perron–Frobenius: the spectral radius of a nonnegative matrix is an eigenvalue

Status: Open.

#404 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 21, 2026

Borcea–Brändén determinantal stability: det(A + Σ zᵢBᵢ) is stable for Hermitian A and PSD Bᵢ

Status: Open.

#400 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 20, 2026

Brändén–Leite Def 3.2 + Thm 3.6/3.7: chain polynomials, subdivision operator, and the induction

Status: Open.

#399 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 20, 2026

Brändén–Leite Thm 2.1/2.6: lower unitriangular TN ⟺ resolvable

Status: Open.

#398 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 20, 2026

[umbrella] Formalize Brändén–Leite: TN matrices give real-rooted chain polynomials

Status: Open.

#395 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 20, 2026

Gantmacher–Krein: totally nonnegative matrices have real nonnegative eigenvalues

Status: Open.

#394 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 20, 2026

A390883: prove real-rootedness of the associahedron toric g-polynomial (Ehrenborg–Hetyei–Readdy Conjecture 11.2) — high priority, novel result

Status: Open.

#392 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 20, 2026

A358628: add proved column generating function and Ehrhart/Legendre structure to OEIS

Status: Open.

#391 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 19, 2026

Formalize weighted matching and independence polynomials (Heilmann–Lieb / Leake–Ryder)

Status: Open.

#375 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 14, 2026

A261318: quantify Euler-operator root separation for cycle sigma rows

Status: Open.

#368 In PerAlexandersson/RealRooted;

· PerAlexandersson opened on Aug 11, 2026