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Again, it is open whether a similar result holds for x-monotone or radial drawings.

For each n, there exists a term order such that a code is 0- or 1-inductively pierced if and only if the reduced Gröbner basis contains binomials of degree 2 or less.

(Analog of Samotij's theorem in Z_2^n). Let n ≥ k ≥ 2 and M be integers. Amongst all families F ⊆ Z_2^n of size |F| = M, centred families minimise the number of 2^k-cubes.

Given a (2s + 1, k, λ) difference set D in a group G, and given a graph Γ of order k and size s, we ask whether it is possibile to label the vertices of Γ with the elements of D is such a way that every non-identity element of G may be…

For any n, p ∈ N with n ≥ p+1, G = P_n^p is equitably k-list arborable if and only if k ≥ ⌈ (p+1)/2 ⌉.

The characteristic set of a path-star tree contains an edge.

We believe c(Q_n)≤ c(Q_n+1) (and similarly for c_L ), but a proof has eluded us.

Is C_4 in DP? More generally, are even cycles in DP?

Let w ∈ S_n be a permutation and l := ℓ(w) be its length. Denote by CS(w) = a = (a_1 ≤ a_2 ≤ … ≤ a_l) ∈ N^l the set of compatible sequences [7] corresponding to permutation w. Define statistics r(a) on the set of all compatible sequences…

Is it possible to partition K_9^3 into stars S_4 so that their mates partition K_9^4? (Star partition without the mate condition is possible [5].)

Can we prove that they are actually convergent to the same limit?

The magnitude homology of a graph obtained by gluing two cycle graphs C_3 along single edges to a single cycle graph C_4 has diagonal magnitude homology provided those triangles are not attached to opposite sides of the 4-cycle.

Does lim_n → ∞ hatr_∞(G_n) = 0 hold for every sequence of graphs (G_n) such that |V(G_n)| → ∞ and Δ(G_n) is bounded as n → ∞? What sequences (G_n) yield lim_n → ∞ hatr_∞(G_n) = 1?

Are there some graphs with diam(G)=n and diam(D_{2}(G))=⌈(1/2)diam(G)⌉+1.

Let f(x_1,…,x_n) be a polynomial over a field F given by (1.1) and (1.2). Provided n≥ k, for any finite subset A of F we have |(f(x_1,…,x_n):x_1,…,x_n∈ A, and x_i≠ x_j if i≠ j)| ≥ minp(F)-llbracket n=2 a_1=-a_2rrbracket,…

The maximum possible load, on any vertex in any graph, is 1/8n^3-O(n^2) .

It is an interesting open problem to classify all fixed points of the twist map, and to determine whether V_k,n is the only totally positive fixed point.

For any d and any connected simple graph G of order d, is i(P_G,m) always a stable polynomial?

We believe that equality should hold in Theorem 1.

Given a finite CW complex X which is not contractible and two ρ-immersed matroids (M, l) and (N, l') such that T_X(M, l) ≃ T_X(N, l'), if there exists a surjective weak map τ: M → N, then τ^# is an isomorphism.