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9

There is also a newer package, HolonomicFunctions, that has an implementation of Chyzak's generalization of Zeilberger's algorithm. To perform the desired task, use the following commands: smnd = Simplify[ G /. HoldPattern[HypergeometricPFQ[pl_List, ql_List, x_]] :> (Times @@ (Pochhammer[#, k] & /@ pl)) / (Times @@ (Pochhammer[#, k] & /@ ql)...


0

Came across this question while looking for something else, but it looks like the graph functions in Mathematica 10 and higher can do this trivially now: m = ({{0, 1, 1, 1}, {1, 0, 1, 1}, {1, 1, 0, 1}, {1, 1, 1, 0}}); g = AdjacencyGraph[m]; FindGraphIsomorphism[g, g, All]; % // Length (* 24 *) %%[[5]] // Normal (* {1 -> 1, 2 -> 4, 3 -> 2, 4 -> 3}...


0

Three observations: Your random process is non-Markovian, i.e. depends on the previous steps The number of states is finite, in your example there are only 90 of them. In view of (i) and (ii) you have a random walk on a tree. You can build the tree explicitly for small systems and study it. But you can also use a brute force approach based on your ...


0

I did genoutcomes[src_, numberforeach_, draws_] := RandomSample[Table[src, {numberforeach}] // Flatten, draws] genoutcomes[{red, green, blue}, 10, 30] yields {red, blue, green, red, red, red, green, blue, green, blue, red, red, \ red, green, green, red, green, red, green, blue, blue, green, blue, \ green, blue, red, blue, green, blue, blue} Hope I did ...


4

A permutation group cannot be partitioned into a list of disjoint permutation groups. Note for example that every permutation group must necessarily contain the identity permutation. But we can partition a group G into a subgroup S and cosets of S in G. For symmetric groups this is easy, because we know that if m < n the SymmetricGroup[m] is a subgroup ...


3

The Subsets function has a third argument to return only some subsets. For example, Subsets[set, All, {k1, k2}] returns the k1th through the k2th subsets. This allows for easy sequential generation in blocks. Please check the documentation for details.



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