Problems

Which posets Q allow for a map φ as above?

The coefficient of q in hatE_k,n(q) is binomnk+1binomnk-2.

they conjectured that C_m × P_n is SEAT if m ≥ 4 even, n ≥ 3 and d ∈ 0, 2;

Does there exist a natural filtration {0=\mathcal{F}{0}\subset \mathcal{F}{1}\subset \cdots } on the ring of semi-invariants SI(Q,\beta) such that for a special quiver Q=T_{n,n,n} and a special dimensional vector \beta , see [14], Section…

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

Nevertheless, we conjecture that their dimension is 2.

In the poset of graphs and cc mappings between them, is every non-degenerate interval nonempty? Does every nondegenerate interval contain an infinite antichain? Does every nondegenerate interval contain every countable poset?

For every r ≥0 and every h≥h0(r), where h0(r) depends on r, there is an integer p1(h,r) depending on h and r, such that for every p≥p1(h,r), each member of K^{-r}(p,p+h) is χ-unique.

Let G be a connected non-transmission-regular graph with n vertices. Then D_1 - λ_1(D) > 1/n+1.

Let K_n_1,n_2,...,n_r be a complete r-partite graph with r vertex sets X_i(i ∈[1,r]) and |X_i|=n_i , ∑_i=1^r=n . Besides (i) and (ii) in Theorem 8, fgndi_∑(K_n_1,n_2,...,n_r)≤ 3 ?

What are the homotopy types of Q_n(Π) ? (in general their order complexes aren't necessarily spheres, or even Cohen-Macaulay)

Another problem worth mentioning is whether the lower bound for c_2(G) still holds without the regularity assumptions, i.e. if we only assume that the graph has large girth and the degree of each vertex is greater than 2.

Let X be a compact Hausdorff space and T:X → X a continuous map. For any open U ⊆ X and any ℓ ∈N , there exists n ∈N with U ∩ T^-nU ∩ T^-2nU ∩… ∩ T^-ℓ nU ≠∅,or (3) T^-inU ∩ T^-jnU=∅ ∀0 ≤ i<j ≤ℓ. (4)

Is this true “for any graph G, dis_s[G] ≤ χ(G)?”

For any nonnegative integer k, does there exist a connected graph G satisfying φ_(2,j)(G) − κ_(2,j)(G) + 1 = k?

Does a Nim-basis, if it exists, necessarily consist of the disjoint unions of circuits of the complex?

Provided lower and upper bounds for f(k).

Is there a graph G such that for any non-empty graph H, we have χ_{td}(H □ G) > χ_{td}(G)?

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

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