Problems

φ(n, m) = n(m-1) + 1.

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.

This partial choice of factors has a unique coherent extension to tildeA .

Do we always have ∂_v,G_B(A)≥ d μ(C(B))^1/d|A|^1-1/d ?

In the general case, for any m > 1, n = 2^m, for any n-tuple of A matrices satisfying (1), does there always exist an n-tuple of B matrices of order c that satisfies construction (H0) under condition (H1), where c = M(n-1), with M defined…

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…

Is C_τ(A_+) always isomorphic to C_π(A_+) ? In other words, is there a bijection f:C_τ→ C_π that satisfies the condition d(x,y)∈ A_+⇔ d(f(x),f(y))∈ A_+?

Suppose we revised our definition of an s-partition so that each part was required to be 2-edge connected, except the small part. What degree of edge connectivity would be required to ensure the existence of an s-partition (if such a…

While it is important to note that twisted subgroups need not be subgroups (e.g., there are small counterexamples in non-abelian groups of order 27 and 75), it could perhaps be the case that L(G) = {|H| : H \subsetneq G} (and thus, our…

It is however conjectured that one of these constructions either “K-groupings” or “J-groupings” will yield a maximum independent set for a given I-graph.

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…

Suppose 17/30≤α≤1 and β>(2 α-1)/4 or 43/120≤α<17/30 and β>(5 α-2)/25 . For all sufficiently large n, a graph of order n in which each set of ⌊α n⌋ vertices spans at least β n^2 edges must contain a triangle.

Let G be a finite transitive group on Ω. If I_Ω(G) > 1/2, then I_Ω(G) = (q+1)/2q, for some q ∈ Q with 2q ∈ N.

Does our improved estimate for the edge isoperimetric inequality in the remark following Theorem 3.1 hold for general B, i.e. do we always have ∂_e,G_B(A)≥ d μ(Z(B))^1/d|A|^1-1/d ?

Assume that p nmid (m-1) and 2 ≤ m ≤ q+1/3. Then the cliques from Proposition 4.6 and Proposition 4.7 are maximal.

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.

Given an arbitrary rational number q ∈ [0,1] does there exist a relevant triple ⟨n,k,⋄⟩ such that q = Ψ(n,k,⋄)/n^k?

There is an isomorphism of graded S_n-modules R_n,k,r≅ R_n,k,r' .

For the case k>5, Corollary 4.19 gives a necessary condition for what kind of cycles can appear in the promotion action on SYT(sc_k) . We do not know if this condition is sufficient.

However, it is unknown whether all finite groups are connected 3-CI-groups, and it is conjectured in [15] that the answer is positive.