Fibonacci semigroups
نویسندگان
چکیده
منابع مشابه
Frobenius numbers of generalized Fibonacci semigroups
The numerical semigroup generated by relatively prime positive integers a1, . . . , an is the set S of all linear combinations of a1, . . . , an with nonnegative integral coefficients. The largest integer which is not an element of S is called the Frobenius number of S. Recently, J. M. Maŕın, J. L. Ramı́rez Alfonśın, and M. P. Revuelta determined the Frobenius number of a Fibonacci semigroup, th...
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The symmetric numerical semigroups S (Fa, Fb, Fc) and S (Lk, Lm, Ln) generated by three Fibonacci (Fa, Fb, Fc) and Lucas (Lk, Lm, Ln) numbers are considered. Based on divisibility properties of the Fibonacci and Lucas numbers we establish necessary and sufficient conditions for both semigroups to be symmetric and calculate their Hilbert generating series, Frobenius numbers and genera.
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In the theory of quasicrystals, one typically deals with coordinates (indices) that lie in some Z-module of rank higher than the dimension of the ambient space, R. Often, these Z-modules are R-modules for some ring R and thereby admit sets of self-similarities (by scaling with elements of R), with a much richer structure than that available for lattices in R. It is natural to study these and ot...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1994
ISSN: 0022-4049
DOI: 10.1016/0022-4049(94)90005-1