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We have not been able to prove either way.

A balanced magic square of order 5 is completely balanced.

Is there a function f(x, y) such that for any graphs G_1 and G_2 we have χ_{td}(G_1 □ G_2) ≤ f(χ_{td}(G_1), χ_{td}(G_2))?

Is the reflexive dimension of the Minkowski sum P + P' bounded by refldim(P) + refldim(P') + c?

We conjecture that in the case of skips of j and j+1 we have in fact equality, and not just a lower bound using K-groupings.

For any nonnegative integer k, does there exist a graph G that satisfies φ_(2,j)(G) − κ_(2,j)(G) + 1 = k?

What is the exact asymptotics of ex_e(G_1, n)?

Let n ≥2 k+1, k ≥1. Let D_k be the set of permutations of S_n with k descents. Let A_k be the set of permutations with k ascents.There is a bijection σ:D_k→ A_k which satisfies σ(x)≥x in weak Bruhat ordering.

We conjecture that i_k(n)/i_k-1(n) is a decreasing function of k for any n.

Characterize non-König-Egerváry graphs satisfying; • varrho_e(G) ≥ m(G) - ξ(G) + ε(G); • varrho_v(G) = n(G) - ξ(G) + ε(G); • varrho_v(G) = α(G) + μ(G) - ξ(G) + ε(G).

For a pr-graph H,B_H has a special bipartite-min ordering if and only if it has a parity-symmetric one.

Conjecture 6.3. We have H_2,1^(k)(x)=frac1+2x^k1-2x+2x^k-2x^k+1.

With what frequencies do each of these 6 cases occur?

After a big number of experiments the author conjectured that for all finite Abelian groups G,all homomorphisms f:G^3→ G and all periodic initial conditions g,h:N→ G , the resulting recurrent double sequence can also be generated by an…

Let t_k,q(n) be defined by (5.1) t_k,q(j) = q^j, for 0 ≤ j ≤ k-1 t_k,q(n) = q ∑_l=0^k-2 (q-1)^l t_k,q(n-(l+2)), for n ≥ k. Then, S_F_q(T_2,3,…,k(n)) = t_k,q(n) for all values of n ≥ k.

However, we conjecture σ_{6}(2^{k}\cdot 3)=8 for all k ∈N.

However, the jury is still out on whether or not any of the 10-point chirotopes are realizable in 3D space.

The question remains, however, is there a transformation G such that G(T(x))= M_{T}(x) ? If so, what is it?

ℓ(7,3)=11.

Is any relation between diam(F_p,q_1∪ F_p,q_2) and diam F_p,q_1+ +diam F_p,q_2 ? Are there any non-trivial p,q_1,q_2 such that these numbers are the same?