A factorization of a permutation into transpositions is called “primitive” if its factors are weakly ordered. We discuss the problem of enumerating primitive factorizations of permutations, and its place in the hierarchy of previously studied factorization problems. Several formulas enumerating minimal primitive and possibly non-minimal primitive factorizations are presented, and interesting co...

We evaluate the sum of a finite group of linear characters of a Hopf algebra, at all grouplike and skew-primitive elements, and mention results for products of skew-primitive elements. Examples include quantum groups associated to semisimple and abelian Lie algebras, and degenerate affine Hecke algebras of reductive type with trivial parameter.

this is the report of a mandibular neuroectodermal/ewing sarcoma in an 8-year-old male cross breed dogthat is unique because of tumor origin location. pedunculated, ulcerative, firm 6.0 × 4.0 × 5.5 cm tumor masseffaced the bone at the rostral part of the mandible and had a white-sanguineous color at cross sectionappearance. histopathologically, small round blue cell tumor was diagnosed. immunoh...

Abstract A graph is edge-primitive if its automorphism group acts primitively on the edge set, and $2$ -arc-transitive transitively set of -arcs. In this paper, we present a classification for those graphs that are have soluble edge-stabilizers.

We show that in any finite field Fq a primitive root can be found in time O(q’ ‘+’ ) Let Fq denote a finite field of q elements. An element 0 E IFq is called a primitive root if it generates the multiplicative group F;,“. We show that a combination of known results on distribution primitive roots and the factorization algorithm of [6] leads to a deterministic algorithm to find a primitive root ...

Importantly, there is no element 1 ≤ k < p − 1 such that a ≡ 1(modp). The concepts presented in the study of primitive elements can be considered special cases of more general idea presented in group theory. Specifically, the primitve element a can be seen as a generator of Zp, we wil discuss this in more detail in the first section of the paper. Primitive elements also have applications in enc...

attributes Involving a significant amount of high-level reasoning about the meaning and purpose of the objects or scenes depicted (e.g. illegal plantation). They are outside the scope of the current research activity. Figure 2. Logical representation of data and derived attributes extraction of primitive features and the reduction of the resulting data into primitive feature clusters. The primi...

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We examine the subgroup D ( G ) of a transitive permutation group which is generated by derangements in . Our main results bound index this subgroup: we conjecture that, if has degree n and not Frobenius group, then | : ? ? 1 ; prove except when primitive affine group. For groups, translate our into an equivalent form regarding H R , where linear on finite vector space elements having eigenvalu...