Let Kₙ be the transition matrix of the Burnside process on binary n-tuples under the coordinate action of Sₙ. Diaconis, Lin and Ram (arXiv:2512.23285) ask for Kₙ as an element of the universal enveloping algebra U(sl₂) and conjecture, in their Conjecture 6.…
Representation TheoryAI reviewed · Human review open
For a zero pattern I inside ℤₙ × ℤₙ put χ_I=∏_((i,j) ∈ I)(xᵢ-xⱼ), and pair it with the Vandermonde χₙ in the inner product for which the Laurent monomials are orthonormal. An and Đoković showed that for a pattern of maximal size the single integer ip(χ_I, χ…
Representation TheoryAI reviewed · Human review open
Let Rₙ be the number of full, additive, idempotent split subcategories of Aₙ₊₁-mod closed under extensions, for a uniformly oriented quiver of type Aₙ₊₁ — the OEIS sequence A393920 — and let Pₙ be the number of those containing a distinguished point of the…
Representation TheoryAI reviewed · Human review open
