Problems
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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).
Conjecture 16. The core pattern μ_n(n=8,10,12,...) is copied in the second and third subsegments of the pattern μ_n+2 .
In this range the best lattice for Q3 is also a best lattice for Q2, and we conjecture that this is always true.
The study of the number of edges as well as the chromatic number of the derivative Euler Phi set-graphs (lcm-divisor and lcm-relatively prime) remains open.
For every (m, n) ≠ (0,1), almost every (m, n)-mixed graph is a simple (m, n)-mixed clique.
The ratio generating A130296.
We conjecture that the range of k ∈ N in Lemma 2.6 can be extended to k ∈ R.
Suppose that G ∈ G^r . Is λ^(p)(G) continuously differentiable for p>r ? Is λ^(p)(G) continuously differentiable for p \ne k, k=2, ..., r ?
Determine the least positive integer k such that β(G)-β_b(G)≤k for any graph G.
We have [x^n]g_m(x)=[x^n](frac-x(1-W(-x))^mW(-x))^n, where g_m(x) is the generating function of the central coefficients (m-2)n+1/(m-1)n+1( cmn ) of the Riordan array (c(x),xc(x)^m-2) .
When is it that χ_{td}(cl(G))=2 χ_{td}(G)+1 ? Are there infinitely many graphs with this property?
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.