Problems

Provided lower and upper bounds for f(k).

it is not known whether \alpha_{\lambda}(k;p) has unimodal coefficients for all \lambda and k.

For each D ∈ D and ψ=ψ_D , there is a unique prime factor Z_ψ(x) of P_ψ(x) such that degZ_ψ equals the number of elements in G ψ .

Perhaps an equally daring conjecture would be that L(G) = {d : d divides |G|}, in which case we would have f(G) = f^{*}(|G|).

Let V be a 2-dimensional subspace in F_p^4, such that 1 ∈ V. Then V is a clique in PP(p^4, p + 1, I) for some I if and only if V = F_p ⊕ aF_p, where a = g^(p+1)k and k is an odd integer.

B(n, m) = n(m-1) + 1.

This results lead us to establish a conjecture that gives us an algebraic and a combinatorial description of the sandpile group of the cone of the hypercube Q_d of dimension d. More precisely, K(c(Q_d)) ≅ bigoplus_i=1^d Z_2i+1^binomdi =…

Let m ≥ 3 be an integer, and let Γ be a graph coprime to K_m such that Aut(Γ) ≠ 1. If Γ is connected and R-thin, then (Γ, K_m) is stable.