Problems

The Möbius function of KC_n alternates in sign for each n ≥ 1.

Let χ(H)≤ k≥ 3 . Then rex(n,H,K_k+1)=(1+o(1))N(H,T(n,k)) .Moreover, if n is sufficiently large and is divisible by k, then rex(n,H,K_k+1)=N(H,T(n,k)) .

Determine the complexity of INDEPENDENT DOMINATION OF DIRECT PRODUCTS

Assume that p nmid (m-1) and 2 ≤ m ≤ q+1/3. Then the cliques from Proposition 4.10 and Proposition 4.13 are maximal.

Any collection of sets with no empty Venn regions is splittable.

If given two positive integers a and b where a ≤ b ≤ 2a, is it possible to find a graph and a permutation α on V(G) such that γ(G)=a and γ(P_α(G))=b for all a,b ∈ N?

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

If L is a set of lines in F_q^3 such that |L|=Ω(q^3) , and such that no plane contains ω(q) lines of L, then |P(L)|≥(1-o(1))q^3 .

The sequence of coefficients of F_n^(a)(x) is unimodal.

Find a derangement σ of the set M of all noncrossing perfect matchings of 1, 2, …, 2n such that ⟨ α, σ(α) ⟩ = 1 for all α ∈ M.

Do there exist polynomials f_{1}(\zeta),f_{2}(\zeta),f_{3}(\zeta) and f_{4}(\zeta) ,corresponding to every pair (a, b), satisfying (33), given as in (15), satisfying (16)and (17), such that f_{1}(1)=0,\quad f_{2}(1)^{2}=a^{2},\quad…

Let G be a finite graph and G = G(min). What condition on the set \mathcal{K}(G) = {K(v) | v \in V(G)} is equivalent to the existence of an endomorphism of G' modulo G?

Is M(u) a CFG or not?

Is this true? “For each positive integer n, there is a graph G with n vertices such that dis[G] - dis_s[G] = Ω(√n).”

Let φ be a primitive binary morphism with an antipalinidromic fixed point u. Then φ or φ^2 is conjugated to a morphism in class A_1 ∪ A_2.

This leaves open the question about the cardinality of the largest set of pairwise divergent infinite permutations.

Assuming that a minimal partition extender exists, is it unique?

α(k, r) = (k - 1)(4r - k - 6) for 5 ≤ r ≤ k ≤ 2r - 4.

Let S be the smallest family of subsets of I such that each t-subset of I occurs in at most \lambda blocks.Then S contains all subsets of size \geqslant(n-r') , where r' is the largest integer satisfying ( cn-t n-t )+( cn-t n-t-1 )+...+(…

Consequently one can ask if there is always an optimal circular permutation of the same form as the pattern.