Möbiova inverzní formule
| Thesis title in Czech: | Möbiova inverzní formule |
|---|---|
| Thesis title in English: | Möbius inversion formula |
| Key words: | Möbiova inverzní formule|kombinatorika |
| English key words: | Möbius inversion formula|combinatorics |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Pavel Růžička, Ph.D. |
| Author: |
| Guidelines |
| Cílem práce studium zobecnění a aplikací Möbiovy inverzní formule. |
| References |
| 1. E.A. Bender, J.R. Goldman, "On the applications of Möbius inversion in combinatorial analysis", Amer. Math. Monthly, 82 (8), 1975, 789–803.
2. P. Hall, "The Eulerian functions of a group". Quart. J. Math. Oxford Ser. 134–151, 1936. 3. G. Rota, "On the Foundations of Combinatorial Theory I. Theory of Möbius Functions", Z. Wahrseheinlichkeitstheorie 2, 1964, 340–368. 4. L.Weisner, "Abstract theory of inversion of finite series". Trans. Am. Math. Soc. 38 (3), 1935, 474–484. 5. L. Weisner, "Some properties of prime-power groups". Trans. Am. Math. Soc. 38 (3), 1935, 485–492 |
| Preliminary scope of work |
| Möbiova inverzní formule byla objevena A.F. Möbiem v roce 1836. Později byla mimo jiné zobecněna na součty indexované lokálně konečnými částečně uspořádanými množinami (E.W. Weisner [4,5], nezávisle P. Hall [2]). Kombinatorické aspekty a význam této formule shrnul v obsáhlém článku G. Rota [3].
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| Preliminary scope of work in English |
| Möbius inversion formula was discovered by A.F. Möbiem in 1836. The formula and its generalizations (e.g E.W. Weisner [4,5], P. Hall [2]) found many applications in various branches of mathematics. A crucial paper dealing with combinatorial aspects of the Möbius inversion formula, published in 1964, is due to G. Rota [3]. |