Problems

The +1 in (3) can be replaced by +1 / 2 (which is best possible).

This raises the question of whether asymptotic separation between n and pdeg(f) is a strictly decreasing function when plotted against sensitivity order.

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

A graph is K 5-friendly if and only if it does not contain any of K_6,C_7^2 and DW_5 as a minor.

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.

Given a cancellative, finitely-generated monoid M in which lcm's exist, is M necessarily a Garside monoid? That is, does there exist a Garside element Δ in M ?

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?

In view of the absence of the Shannon effect and Kozik’s result on the limiting distributions it seems reasonable that asymptotically almost all functions have polynomial complexity.

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.

Let m > n, and let b = v_i_i=1^n be a basis for Z^n. For a finite index subgroup Σ < Z^n consider the subset S_Z^n/Σ(b, m) = s ∈ S_Z^n/Σ(m) : s ⊃ b mod Σ (that is, we restrict attention to the generating sets which contain the reduction of…

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].