In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice that does not visit the same point more than once. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. As such, SAWs are often used to model the real-life behaviour of chain-like entities such as solvents and polymers, whose physical volume prohibits multiple occupation of the same spatial point.

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  • In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice that does not visit the same point more than once. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. As such, SAWs are often used to model the real-life behaviour of chain-like entities such as solvents and polymers, whose physical volume prohibits multiple occupation of the same spatial point. In computational physics a self-avoiding walk is a chain-like path in <math>\mathbb{R}^2</math> or <math>\mathbb{R}^3</math> with a certain number of nodes, typically a fixed step length and has the imperative property that it doesn't cross itself or another walk. A system of self-avoiding walks satisfies the so called excluded volume condition. A self-avoiding walk is interesting for simulations because its properties cannot be calculated analytically, thus it is very helpful to understand polymers, e.g. DNA molecules. SAWs SAPs play a central role in the modelling of the topological and knot-theoretic behaviour of thread- and loop-like molecules such as proteins. Calculating the number of self-avoiding walks in any given lattice is a common computational problem. There is currently no known formula for determining the number of self-avoiding walks, although there are rigorous methods for approximating them. Finding the number of such paths is conjectured to be an NP-hard problem. For self-avoiding walks from one diagonal to the other, with only moves in the positive direction, there are exactly <math>{m+n \choose m,n}</math> paths for an m × n square lattice.
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  • Self-Avoiding Walk
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  • Self-AvoidingWalk
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  • In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice that does not visit the same point more than once. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. As such, SAWs are often used to model the real-life behaviour of chain-like entities such as solvents and polymers, whose physical volume prohibits multiple occupation of the same spatial point.
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  • Self-avoiding walk
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