Nó inversível

Em matemática, especialmente na área de topologia conhecida como teoria do nó, onde nó inversível tem a propriedade de um nó que pode ser continuamente deformado para si, mas com a sua orientação invertida. Um nó que não pode ser inversível é qualquer nó que não têm esta propriedade. O inversível de um nó é um nó invariável. Um nó pode ser inversível quando ele é equivalente a um nó que pode ser inversível.

Há apenas cinco nó tipos de simetria, indicado pela quiralidade e a inversão: totalmente quirais, reversível, de forma positiva amphichiral não inversível, negativamente amphichiral não inversível, e totalmente amphichiral pode ser inversível.[1]

Fundo

Número de invertível e não pode ser invertida nós para cada cruzamento número
Número de cruzamentos 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Sequência na OEIS
Não pode ser invertida nós 0 0 0 0 0 1 2 33 187 1144 6919 38118 226581 1309875 A052402
Pode ser invertida nós 1 1 2 3 7 20 47 132 365 1032 3069 8854 26712 78830 A052403

Ele tem sido conhecido que a maioria de nós simples, como o trevo de nó e a figura-oito nó são inversíveis. Em 1962, Ralph Fox sugeriu que não era possível o inversível de alguns nós, mas não foi provado que não pode ser inversíveis nós que existem até H. F. Trotter que descobriu uma infinita família de nós pretzel que eram não-inversíveis em 1963.[2]  Agora, de quase todos nós não podem ser inversíveis.[3]

Referências

  1. ↑ Hoste, Jim; Thistlethwaite, Morwen; Weeks, Jeff (1998), «The first 1,701,936 knots» (PDF), The Mathematical Intelligencer, 20 (4): 33–48, doi:10.1007/BF03025227, consultado em 11 de julho de 2017, cópia arquivada (PDF) em 15 de dezembro de 2013 
  2. ↑ Trotter, H. F. (1963), «Non-invertible knots exist», Topology, 2: 275–280, doi:10.1016/0040-9383(63)90011-9 
  3. ↑ Murasugi, Kunio (2007), Knot Theory and Its Applications, ISBN 9780817647186, Springer6, p. 45 
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