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Arithmetic Varieties of Numerical Semigroups
In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the...
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On the arithmetic-geometric spectral radius of bicyclic graphs
The arithmetic-geometric spectral radius of a graph G is the largest eigenvalue of the arithmetic-geometric matrix of G whose ( u , v )-entry is
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Extremal arithmetic–geometric spectral radius of unicyclic graphs
Spectral graph theory has been widely used in many fields, including network science, chemistry, physics, biology and sociology. Spectral extremal...
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Hyperbolic Punctured Spheres Without Arithmetic Systole Maximizers
We find bounds for the length of the systole—the shortest essential, non-peripheral closed curve—for arithmetic punctured spheres with n cusps, for
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Arithmetic subtrees in large subsets of products of trees
Furstenberg-Weiss have extended Szemerédi’s theorem on arithmetic progressions to trees by showing that a large subset of the tree contains...
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Intuitionistic sets and numbers: small set theory and Heyting arithmetic
It has long been known that (classical) Peano arithmetic is, in some strong sense, “equivalent” to the variant of (classical) Zermelo–Fraenkel set...
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Models of Arithmetic and Independence Results
The Paris–Harrington variant of Ramsey’s Theorem is proved independent of Peano Arithmetic by model theoretic methods. As a warm-up, we give model...
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Bounds for the geometric–arithmetic index of unicyclic graphs
We present lower and upper bounds for the geometric–arithmetic index of unicyclic graphs and provide extremal graphs for the corresponding bounds.
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Incompleteness of Arithmetic from the Viewpoint of Diophantine Set Theory
The authors analyze Diophantine sets and show that all recursively enumerable sets are Diophantine. Based on the classical results from the theory of...
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Continuous Mean Distance of a Weighted Graph
We study the concept of the continuous mean distance of a weighted graph. For connected unweighted graphs, the mean distance can be defined as the...
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Arithmetic
The standard model of arithmetic is the structure $$\mathfrak {N}= \langle \omega...
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Induced arithmetic removal: complexity 1 patterns over finite fields
We prove an arithmetic analog of the induced graph removal lemma for complexity 1 patterns over finite fields. Informally speaking, we show that...
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Graph Models for Contextual Intention Prediction in Dialog Systems
AbstractThe paper introduces a novel methodology for predicting intentions in dialog systems through a graph-based approach. This methodology...
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The arithmetic topology of genetic alignments
We propose a novel mathematical paradigm for the study of genetic variation in sequence alignments. This framework originates from extending the...
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Arithmetic fundamental lemma for the spherical Hecke algebra
We define Hecke correspondences and Hecke operators on unitary RZ spaces and study their basic geometric properties, including a commutativity...