We point out an interplay between Fq-Frobenius non-classical plane curves and complete (k, d)-arcs in P2(Fq). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q − d + 2) and d = (q − 1)/(q − 1), q being a power of the characteristic. In addi...

Let A denote the ring of differential operators on the affine line with its two usual generators t and d dt given degrees +1 and −1 respectively. Let X be the stack having coarse moduli space the affine line Spec k[z] and isotropy groups Z/2 at each integer point. Then the category of graded A-modules is equivalent to the category of quasicoherent sheaves on X .

We suppose that p = 2α3β +1, where α ≥ 1, β ≥ 0, and p ≥ 7 is a prime number. Then we prove that the simple groups An, where n = p,p+1, or p+2, and finite groups Sn, where n = p,p+1, are also uniquely determined by their order components. As corollaries of these results, the validity of a conjecture of J. G. Thompson and a conjecture of Shi and Bi (1990) both on An, where n= p,p+1, or p+2, is o...

Given a family F and a host graph H, a graph G ⊆ H is F-saturated relative to H if no subgraph of G lies in F but adding any edge from E(H)−E(G) to G creates such a subgraph. In the F-saturation game on H, players Max and Min alternately add edges of H to G, avoiding subgraphs in F , until G becomes F-saturated relative to H. They aim to maximize or minimize the length of the game, respectively...

Applying the techniques of nonabelian duality to a system of Majorana fermions in 1+1 dimensions, invariant under a nonabelian group O L (N) × O R (N), we obtain the level-one Wess-Zumino-Witten model as the dual theory. This makes nonabelian bosonization a particular case of a nonabelian duality transformation, generalizing our previous result for the abelian case.

We show that any set of n pairwise disjoint ovals in a finite projective plane of even order has a unique common tangent. As a consequence, any set of q+1 pairwise disjoint ovoids in PG(3, q), q even, has exactly q2+1 common tangent lines, constituting a regular spread. Also, if q−1 ovoids in PG(3, q) intersect pairwise exactly in two given points x ̸= y and share two tangent planes πx, πy at th...

1 Department of Computer Science and Engineering, Michigan State University, East Lansing, MI 48824, USA; [email protected] 2 BEACON Center for the Study of Evolution in Action, Michigan State University, East Lansing, MI 48824, USA 3 Department of Microbiology & Molecular Genetics, Michigan State University, East Lansing, MI 48824, USA; [email protected] 4 Department of Integrative Biology, Michigan St...

In this paper n denotes a natural number, X denotes a set, and F1, G1 denote families of subsets of X. Let us consider X, F1. We say that F1 is finite-order if and only if: (Def. 1) There exists n such that for every G1 such that G1 ⊆ F1 and n ∈ CardG1 holds ⋂ G1 is empty. Let us consider X. Observe that there exists a family of subsets of X which is finite-order and every family of subsets of ...