Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
29 problems
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.
B(n, m) = n(m-1) + 1.
However, it is unknown whether all finite groups are connected 3-CI-groups, and it is conjectured in [15] that the answer is positive.
This results lead us to establish a conjecture that gives us an algebraic and a combinatorial description of the sandpile group of the cone of the hypercube Q_d of dimension d. More precisely, K(c(Q_d)) ≅ bigoplus_i=1^d Z_2i+1^binomdi =…
It is natural to conjecture that ker(f^*)=Z_d+2^2⊕ Z_d(d+2)^β(G)-2 holds for non-bipartite graphs in general.
Let m ≥ 3 be an integer, and let Γ be a graph coprime to K_m such that Aut(Γ) ≠ 1. If Γ is connected and R-thin, then (Γ, K_m) is stable.