#Riffle mathematica manual
Série B, vol. 9, Coimbra: Universidade de Coimbra Departamento de Matemática, MR 1399082 substitute for general Mathematica manual or Wolfram Language & System Documentation. (1995), Shuffle algebras, Lie algebras and quantum groups, Textos de Matemática.
#Riffle mathematica mac
Eilenberg, Samuel Mac Lane, Saunders (1953), "On the groups of H(Π,n).The infiltration product is also commutative and associative. It is defined inductively on words over an alphabet A byįa ↑ ga = ( f ↑ ga) a + ( fa ↑ g) a + ( f ↑ g) a fa ↑ gb = ( f ↑ gb) a + ( fa ↑ g) bĪb ↑ ab = ab + 2 aab + 2 abb + 4 aabb + 2 abab ab ↑ ba = aba + bab + abab + 2 abba + 2 baab + baba Mathematica has a number of useful formatting heads for arbitrary expressions. The closely related infiltration product was introduced by Chen, Fox & Lyndon (1958). Mathematica Programming Higher-Level Functionality. The shuffle product of two words in some alphabet is often denoted by the shuffle product symbol ⧢ ( Unicode character U+29E2 SHUFFLE PRODUCT, derived from the Cyrillic letter ⟨ш⟩ sha).
The product is commutative and associative. The name "shuffle product" refers to the fact that the product can be thought of as a sum over all ways of riffle shuffling two words together: this is the riffle shuffle permutation. The shuffle product was introduced by Eilenberg & Mac Lane (1953). Where ε is the empty word, a and b are single elements, and u and v are arbitrary words. For any given split the p cards in one deck maintain their order but can occupy any p slots in the resulting deck, so there are ( n p) resulting decks that can result from the division. It may be defined inductively by u ⧢ ε = ε ⧢ u = u ua ⧢ vb = ( u ⧢ vb) a + ( ua ⧢ v) b In the riffle shuffle you split the deck into a deck consisting of the p top cards and another consisting of the bottom q cards with p + q n. The shuffle product of words of lengths m and n is a sum over the ( m+ n)! / m! n! ways of interleaving the two words, as shown in the following examples:Īb ⧢ xy = abxy + axby + xaby + axyb + xayb + xyab aaa ⧢ aa = 10 aaaaa
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