On A Combinatorial Problem Connected withFactorizations
On a complete set of operations for factorizing codes
It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set of operations exists such that each factorizing code can be obtained by using the operations in and starting with prefix or suffix codes. is named here a complete set of operations (for factorizing codes). We show...
On a complete set of operations for factorizing codes
It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set O of operations exists such that each factorizing code can be obtained by using the operations in O and starting with prefix or suffix codes. O is named here a complete set of operations (for factorizing codes). We show...
On a conjecture of Alperin and McKay.
On a conjecture of Brown.
On a conjecture of Erdös and Heilbronn
On a conjecture of Hamidoune for subsequence sums.
On a conjecture of Kottwitz and Rapoport
We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur’s Inequality for all (connected) split and quasi-split unramified reductive groups. Our results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.
On a conjecture of M. E. Watkins on graphical regular representations of finite groups
On a Conjecture of Magnus on the Hurwitz Monodromy Group.
On a conjecture of Rhodes.
On a conjecture of the semigroup of fully indecomposable relations
On a Conjecture of Zassenhaus on Torsion Units in Integral Group Rings.
On a connection between nilpotent groups and Lie rings.
On a connection of number theory with graph theory
We assign to each positive integer a digraph whose set of vertices is and for which there is a directed edge from to if . We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.
On a constant of Turán and Erdös
On a construction of semigroups
On a Construction of Some Semigroups
On a covering group theorem and its applications.
On a cubic Hecke algebra associated with the quantum group
We define an operator α on ℂ³ ⊗ ℂ³ associated with the quantum group , which satisfies the Yang-Baxter equation and a cubic equation (α² - 1)(α + q²) = 0. This operator can be extended to a family of operators on with 0 ≤ j ≤ n - 2. These operators generate the cubic Hecke algebra associated with the quantum group . The purpose of this note is to present the construction.