Problems

We conjecture that this is true for all q.

In which condition power graph P(G) of a non-degenerate gyrogroup G is complete?

Let V be a 2-dimensional subspace in F_p^4, such that 1 ∈ V. Then V is a clique in PP(p^4, p + 1, I) for some I if and only if V = F_p ⊕ aF_p, where a = g^(p+1)k and k is an odd integer.

If a neural code is labeled such that the i^th neuron is added as a piercing at the i^th step, then its toric ideal has a quadratic Gröbner basis with respect to the term order prec.

Specifically, we conjecture that similar processes will work for cycle pendant stars up to stars of size 15.

We conjecture that i_k(n)/i_k-1(n) is a decreasing function of k for any n.

After a big number of experiments the author conjectured that for all finite Abelian groups G,all homomorphisms f:G^3→ G and all periodic initial conditions g,h:N→ G , the resulting recurrent double sequence can also be generated by an…

Let t_k,q(n) be defined by (5.1) t_k,q(j) = q^j, for 0 ≤ j ≤ k-1 t_k,q(n) = q ∑_l=0^k-2 (q-1)^l t_k,q(n-(l+2)), for n ≥ k. Then, S_F_q(T_2,3,…,k(n)) = t_k,q(n) for all values of n ≥ k.

Find other possible values of the parameter d and the corresponding d-antimagic labeling of type (1, 1, 1) for the generalized Petersen graph P(n, 2).

Construct and analyze analogues of the Hanoi graph H_n in variants 4 and 5. Is there a generalization of the Lucas Correspondence that works here?

Can you show F(n; 2)< (1+ε)n/2 ? What about larger values of t ?

For every 2-coloring of the positive integers there exist positive integers a,d such that the elements of the arithmetic progression a,a+d,...,a+d^2 all are colored the same.

Let C be a projective [n,k]_q three-weight code with non-zero weights w_1 < w_2 < w_3 satisfying w_1 + w_2 + w_3 = 3(1-1/q)n. Then w_2 = (1-1/q)n. Moreover, w_1 = w_2 - t and w_3 = w_2 + t, where t is a power of the characteristic p of F_q.

For any ℓ ∈N and any (not necessarily finite) partition N=∪_i=1^∞C_i , there exists d ∈N such that either (i) for some i_0∈N we have C_i_0∩(C_i_0-d)∩(C_i_0-2d)∩… ∩(C_i_0-ℓ d)≠∅ , or (ii) for every i ∈N we have (C_i-jd)∩(C_i-kd)=∅ for all…

If k is a power of a prime, P_L_k(G,k)=P_DP(G,k).

Conjecture 1.6.1. The polynomial f_m(b,q) has the form f_m(b,q)=∑_i=0^binomm2(1-q)^m-y^(i)g_m,i(q)b^i where y(n)=⌊frac√8n+12⌋ and g_m,i(q) are polynomials. Further, with <_k^n> denot ing the Eulerian numbers ^3…

B(n, m) = n(m-1) + 1.

Based upon the results generated from our Sage script, we submit as a conjecture that these graphs constructed be the smallest graphs (by order) that have characteristic-dependent well-covered dimension for any given characteristic.

Let δ≥ 3 be an integer. Does there exist a δ -chromatic quadruple system Q such that χ(K(Q))=δ ?

the existence of such an f has been proved, but uniqueness in T_0 has not.