Problems

All perfect strategies of G(G,b) have classical correlation matrices if and only if b has even parity.

lim_l → ∞limsup_n → ∞P_n^av(τ)(A_l;k_n^(n))=0, for all τ ∈ ∪_m=2^∞S_m and for all k_n.

From this, we (very strongly) conjecture that root bifurcating Greg trees have an asymptotic probability of above (and close to) 0.606.

If p=, then lim_n →∞fracs_n^+(p)n!=1/2 .

An obvious open question is whether we have π_(1,1,1)-qr(F)leqslant π_2(F).

For every (m, n) ≠ (0,1), almost every (m, n)-mixed graph is a simple (m, n)-mixed clique.

As n → ∞ the fraction of graphs that satisfy virial positivity approaches one.

There is a constant K such that for every 2-edge-connected plane graph G it holds fep(G) ≤ K.

Given r random vertices v_1,...,v_r of C^d , what is the expected number of 0 / 1-vectors in the affine subspace spanned by these vectors?

Is it true that f_DR^2(n,C)≈3/2n ? If not, can one prove at least, that f_DR^2(n,C)<(2-c)n? (34)

Let X,barψ be as in Lemma 6.2, and suppose that the roots of ∑_k=0^νp_kx^k are real. Then σ_ψ^2σ_X^2≥μ^4ν^-2 .

Is the Merino–Welsh conjecture true for binary matroids?

It would thus be natural to conjecture that T(H) = Θ(n!/2^e(H)) for, say, all (ε, k)-consistent orientations with n vertices.

For any positive integers k and n satisfying k < n, and any alternating function f: [k] × [k] → Z_n, there exists a permutation π ∈ S_k such that d_π(i, j) ≠ f(i, j) pmodn, for all distinct i, j ∈ [k].

Let f be a finite field. Suppose barX, barY, barα, and barZ_f are random variables with values in f; barα is distributed with respect to the probability counting measure on the set f^× of non-zero elements of f, and barZ_f is distributed…

What is H(n;a_1,a_2,...,a_k) ? Is the upper bound given in Theorem 16 tight?

Suppose now that b ≤ a < s, and m ≫ n^1+s-1. Then satex(n, K_1,s : m, K_a,b) = (1 + o(1)) minN(K_a,b, K_q^*), N(K_a,b, overlineK_r^*), where q = mint ∈ Z : N(K_1,s, K_t) ≥ m and r = mint ∈ Z : N(K_1,s, overlineK_t) > m.

Do subcubic graphs have exponentially independent sets of linear order?

Are there any other sequences (a_n)_n ∈N of integers appearing 'naturally'with the property that there exists a real α>0 such that (α a_nbmod 2 π)_n=1^∞ has an absolutely continuous non-uniform distribution?

Let G=(V, E) be a locally finite, recurrent graph which is quasi-isometric to R. Let h be a harmonic function on G, and suppose that for some finite cut E(X, Y) separating the two ends of G we have ∂h(X,Y)=0. Then h is either constant or…