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Fibonacci-like behavior of the number of numerical semigroups of a given genus
Abstract We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. TheExpand
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Peer-to-Peer Private Information Retrieval
TLDR
A peer-to-peer PIR system is described in this paper which relies on an underlying combinatorial structure to reduce the required key material and increase availability. Expand
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Bounds on the Number of Numerical Semigroups of a Given Genus
TLDR
We prove that numerical semigroups of genus g behave asymptotically as the Fibonacci numbers. Expand
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User-private information retrieval based on a peer-to-peer community
TLDR
A peer-to-peer UPIR system is described in this paper which relies on an underlying combinatorial structure to reduce the required key material and increase availability. Expand
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Optimal configurations for peer-to-peer user-private information retrieval
TLDR
We characterize the optimal configurations for the P2P UPIR and see the relationship with the projective planes as described in finite geometry. Expand
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The semigroup of combinatorial configurations
TLDR
We elaborate on the existence and construction of the so-called combinatorial configurations. Expand
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On query self-submission in peer-to-peer user-private information retrieval
TLDR
We propose a modification of the P2P UPIR protocol in which the users form a peer-to-peer network over which they collaborate in protecting the privacy of each other. Expand
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Patterns on numerical semigroups
We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of numericalExpand
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A bibliometric index based on the collaboration distance between cited and citing authors
TLDR
We present a new index, the c-index, in which the evaluated objects are the citations received by an author, a group of authors, a journal, etc., the quality function of a citation is the collaboration distance between the authors of the cited and the citing papers, and the sentencing line can take slopes between 0 and ∞. Expand
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Unique Decoding of Plane AG Codes via Interpolation
TLDR
We present a unique decoding algorithm of algebraic geometry (AG) codes on plane curves, Hermitian codes in particular, from an interpolation point of view, which corrects errors of weight up to half of the order bound on the minimum distance of the AG code. Expand
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