Calculating Complete Lists of Belyi Pairs

Adrianov, N. M.; Shabat, G. B.

doi:10.3390/math10020258

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…A simpler example is the representation of a representation of a finite number of finite graphs justified by a computer calculation, and the assertion that these graphs exhaust all possibilities for the realization of certain conditions (cf. [49]).…”

Section: Visualization In a Mathematical Experiments And Mathematical...mentioning

confidence: 99%

The Work of a Mathematician As a Prefiguring of Mastering Mathematics by Students: The Role of Experiments

Vishnyakov,

Semenov,

Shabat

2023

Dokl. Math.

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This paper considers an approach to mathematical education adequate to the task of developing mathematics and its applications in the 21th century. This approach is based on improving the efficiency of the educational process by maintaining the motivation of students of various categories. The basis for the formation of motivation is, on the one hand, independent design; invention of mathematical objects, methods of action, and models of the world around us; and the discovery of facts of mathematical reality and, on the other hand, solving of new, unexpected, and feasible tasks for the student. The student’s work is similar to the work of a mathematician–researcher and programmer. The possibilities of research work in educational mathematics are significantly expanded due to computer-based intramathematic experiments. Debugging a computer program is a special kind of mathematical experiment.

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Section: Visualization In a Mathematical Experiments And Mathematical...mentioning

confidence: 99%

The Work of a Mathematician As a Prefiguring of Mastering Mathematics by Students: The Role of Experiments

Vishnyakov,

Semenov,

Shabat

2023

Dokl. Math.

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“…Systematic cataloging of Belyi maps is an active research undertaking [MSSV19,AS22]. Contributing to this venture, this article considers comprehensively Belyi maps φ : P 1 → P 1 of the form φ(x) = (1 − x) p (1 − λx) q G m (x) r (1.1)…”

Section: Introductionmentioning

confidence: 99%

Genus one Belyi maps by quadratic correspondences

Vidūnas

2020

Int. J. Math.

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We present a method of obtaining a Belyi map on an elliptic curve from that on the Riemann sphere. This is done by writing the former as a radical of the latter, which we call a quadratic correspondence, with the radical determining the elliptic curve. With a host of examples of various degrees we demonstrate that the correspondence is an efficient way of obtaining genus one Belyi maps. As applications, we find the Belyi maps for the dessins d'enfant which have arisen as brane-tilings in the physics community, including ones, such as the so-called suspended pinched point, which have been a standing challenge for a number of years.

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The Work of a Mathematician as a Proimage of the Mastering of Mathematics by Students. The Role of the Experiment

Vishnyakov,

Semenov,

Shabat

2023

Doklady Rossijskoj akademii nauk. Matematika, informatika, proc

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The paper considers an approach to mathematical education adequate to the task of developing mathematics and its applications in the XXI century. This approach is based on improving the efficiency of the educational process by maintaining the motivation of students of various categories. The basis for the formation of motivation is, on the one hand, independent design, invention of mathematical objects, methods of action and models of the world around us, the discovery of facts of mathematical reality. On the other hand, it is solving of new, unexpected, feasible tasks for the student. In the described perspective, the student’s work is similar to the work of a mathematician-researcher and programmer. The possibilities of research activity in educational mathematics are significantly expanded due to computer-based intra-mathematic experiment. A special kind of mathematical experiment is debugging a computer program.

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Calculating Complete Lists of Belyi Pairs

Cited by 3 publications

References 25 publications

The Work of a Mathematician As a Prefiguring of Mastering Mathematics by Students: The Role of Experiments

The Work of a Mathematician As a Prefiguring of Mastering Mathematics by Students: The Role of Experiments

Genus one Belyi maps by quadratic correspondences

The Work of a Mathematician as a Proimage of the Mastering of Mathematics by Students. The Role of the Experiment

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