On A Combinatorial Problem Connected withFactorizations
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Weidong Gao (1997)
Colloquium Mathematicae
Clelia De Felice (2006)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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...
Clelia De Felice (2010)
RAIRO - Theoretical Informatics and Applications
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...
E. Szemerédi (1970)
Acta Arithmetica
Grynkiewicz, David J. (2005)
Integers
Lawrence Somer, Michal Křížek (2004)
Czechoslovak Mathematical Journal
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.
Sándor Szabó (1989)
Aequationes mathematicae
Obaid, Evelyn E. (1986)
International Journal of Mathematics and Mathematical Sciences
W. Gao, Y. O. Hamidoune (1999)
Acta Arithmetica
Giampiero Chiaselotti (2002)
Acta Arithmetica
Gábor Czédli, Géza Takách (2000)
Discussiones Mathematicae - General Algebra and Applications
An elementary proof is given for Hutchinson's duality theorem, which states that if a lattice identity λ holds in all submodule lattices of modules over a ring R with unit element then so does the dual of λ.
D. J. Grynkiewicz, O. Ordaz, M. T. Varela, F. Villarroel (2007)
Acta Arithmetica
Obaid, Evelyn E. (1989)
International Journal of Mathematics and Mathematical Sciences
Markku Niemenmaa (2010)
Commentationes Mathematicae Universitatis Carolinae
We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order are centrally nilpotent of class at most two.
Wolfgang Alexander Schmid (2005)
Mathematica Slovaca
Vladimír Puš (1991)
Czechoslovak Mathematical Journal
Wang, Guoqing (2008)
Integers
Lawrence Somer, Michal Křížek (2007)
Commentationes Mathematicae Universitatis Carolinae
We assign to each pair of positive integers and a digraph whose set of vertices is and for which there is a directed edge from to if . The digraph is semiregular if there exists a positive integer such that each vertex of the digraph has indegree or 0. Generalizing earlier results of the authors for the case in which , we characterize all semiregular digraphs when is arbitrary.
Weidong Gao, Yuanlin Li, Pingping Zhao, Jujuan Zhuang (2016)
Colloquium Mathematicae
Let G be an additive finite abelian group. For every positive integer ℓ, let be the smallest positive integer t such that each sequence S over G of length |S| ≥ t has a nonempty zero-sum subsequence of length not equal to ℓ. In this paper, we determine for certain finite groups, including cyclic groups, the groups and elementary abelian 2-groups. Following Girard, we define disc(G) as the smallest positive integer t such that every sequence S over G with |S| ≥ t has nonempty zero-sum subsequences...
Gao, W.D., Hou, Q.H., Schmid, W.A., Thangadurai, R. (2007)
Integers
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