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Topic: Factoradic

	PlanetMath: unambiguity of factorial base representation
		is the factoradic representation of a positive integer
		Cross-references: property, digits, infinite descent, complete, without loss of generality, side, bound, definition, representation, factoradic, telescoping sum, equation, limit, sum, integers, positive
		This is version 11 of unambiguity of factorial base representation, born on 2007-01-30, modified 2007-01-31.
	planetmath.org /encyclopedia/UnambiguityOfFactorialBaseRepresentation.html (178 words)

	Science Fair Projects - Factoradic
		Factoradics provide a lexicographical index for permutations, so they have potential application to computer security.
		The second factoradic digit if "0" then selects for the second permutation digit the first (0-indexed) digit from the shorter list and removes it, or if "1" selects the second (1-indexed) digit from the shorter list and removes it.
		The third factoradic digit must be "0", but by now the list is only one item long, so that last remaining item is selected as the last permutation digit.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Factoradic (699 words)

	Factoradic - Wikipedia, the free encyclopedia
		In combinatorial mathematics, the factoradic is a specially constructed number.
		The idea of the factoradic is closely linked to that of the Lehmer code.
		The origins of the term 'factoradic' are obscure.
	en.wikipedia.org /wiki/Factoradic (548 words)

	[No title]
		We describe an algorithm whereby a series of permutations are generated by operations of a set of factoradics, which comprise a meta-key.
		Primary Jump Key: Used to compute the factoradic from which is generated the next function Fp, after the requisite number of iterations have been executed.
		The key to the addition process is that whenever the sum of two digits exceeds their “place number” then the value is the sum modulo (place number +1) and a carry is generated.
	faculty.kutztown.edu /rieksts/factoradic/PACISEFactoradic.doc (2036 words)

	Not Overlooking Much » Blog Archive » Factoradics in Python
		A factoradic is a special way to represent any non-negative integer.
		Factoradics can be used to create a two-way mapping from an integer to a particular permutation of a set, and from a particular permutation of a set to an integer.
		First, we need to calculate the factoradic representation of 53, which is [2,0,2,1,0].
	blog.hill-street.net /?p=5 (959 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		If you have foo = Permutation(['a','Fred',23,None]) the possible indices are numbered 0 to 23 (0 to 4!-1) sam = foo.permutation(10) mary = foo.permutation(4) sam is ['Fred', None, 'a', 23] mary is ['a', None,'Fred', 23] An interesting thing about the factoradic method is its reversibility.
		If you have a list: ['a','Fred',23,None] and you are presented with an ordering: [23,'a',None,'Fred'] the factoradic method can algorithmically determine that this ordering is index 13 of 24 of the possible permutations, without going forward through your generating algorithm to get there.
		Works by the factoradic method, which provides reversibility.""" _order = None def __init__(self,data=None): if data: self.data = list(data) else: self.data = [] def getOrder(self): if not self._order: self._order = len(self.data) return self._order def setData(self,data): self.data = data self._order = None def permutationIndices(self,index): """calculate the permutation indices of self from index.
	zif.hill-street.net /factoradic/factoradic.py (856 words)

	Using Permutations in .NET for Improved Systems Security
		The factoradic of an integer is its representation based on a variable base corresponding to the values of n factorial.
		The clever and efficient way to derive the kth permutation of order n is to first find the factoradic of k and then to generate the corresponding permutation from the factoradic.
		An alternative that merits investigation is to take the given permutation, reverse compute its factoradic, reverse compute the corresponding k from the factoradic, add 1 to k, compute the factoradic of k+1, and then compute the corresponding permutation.
	msdn.microsoft.com /library/default.asp?url=/library/en-us/dnnetsec/html/permutations.asp (4534 words)

	van NovaLoka
		Scaling back and forth between levels of operators is the very property that makes numbers practical in use.
		Because we have little experience beyond our radix perspective, let's study an alternative, combinatorial system to do arithmetic, more suited for large numbers: The Factoradic number system, based on the factorial numbers:
		Factoradic numbers are not quite up to the task of expressing
	blogger.xs4all.nl /novaloka (7096 words)

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	accommodation-what-whistler.blogspot.com (749 words)

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