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The shuffle algebra on the alphabet A is defined to be the additive group R endowed with ш as multiplication. Radford's theorem [16] now states that the Lyndon words are algebraically independent elements of this shuffle algebra, and generate it; thus, the shuffle algebra is isomorphic to a polynomial ring over k , with the indeterminates ...
Random permutation. A random permutation is a random ordering of a set of objects, that is, a permutation -valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and simulation. A good example of a random permutation is the shuffling of a deck of ...
The Lie algebra L is called free on X if. i {\displaystyle i} is the universal morphism; that is, if for any Lie algebra A with a morphism of sets. f : X → A {\displaystyle f\colon X\to A} , there is a unique Lie algebra morphism. g : L → A {\displaystyle g\colon L\to A} such that.
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Just Words. If you love Scrabble, you'll love the wonderful word game fun of Just Words. Play Just Words free online! By Masque Publishing. Advertisement. Advertisement. Feedback. Help. Join AOL.
ROT13 ( Rotate13, " rotate by 13 places ", sometimes hyphenated ROT-13) is a simple letter substitution cipher that replaces a letter with the 13th letter after it in the Latin alphabet. ROT13 is a special case of the Caesar cipher which was developed in ancient Rome. Because there are 26 letters (2×13) in the basic Latin alphabet, ROT13 is ...
Pinochle. Aces around, dix or double pinochles. Score points by trick-taking and also by forming combinations of cards into melds. By Masque Publishing. Advertisement. Advertisement. Feedback. Help.
The shuffle algebra on a finite set is the graded dual of the universal enveloping algebra of the free Lie algebra on the set. Over the rational numbers, the shuffle algebra is isomorphic to the polynomial algebra in the Lyndon words . The shuffle product occurs in generic settings in non-commutative algebras; this is because it is able to ...
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