combstruct vs. MC vs. AC

[Ralf Hemmecke]

Dear Nicolas,

In Maple help

maplehelp(combstruct[specification])

I can find

(labeled)
F=Set(Set(Z,card>=1)) set partitions

(unlabeled)
A=Set(Sequence(Z,card>=1)) integer partition

How would the same be done in MuPAD-Combinat? Of course, MC has this
builtin, but if you have to define it via a grammar, how would that look
like?

Asking more generally, is MC like combstruct with respect to the
non-correspondence of the labelled and unlabelled situation?

You certainly know better than me that integer partitions are the
isomorphism types of set partitions. Why is this not reflected in the
grammar? With species it is.

Ralf

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[Nicolas M. Thiery]

Post by Ralf Hemmecke
In Maple help
maplehelp(combstruct[specification])
I can find
(labeled)
F=Set(Set(Z,card>=1)) set partitions
(unlabeled)
A=Set(Sequence(Z,card>=1)) integer partition

If you want to highlight the species correspondence, you could also
reuse the same grammar:

A=Set(Set(Z,card>=1))

In the unlabeled case, this is equivalent!

Post by Ralf Hemmecke

IntPart::count(n) $ n=0..10

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42

Post by Ralf Hemmecke

combinat::partitions::count(n) $ n=0..10

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42

Post by Ralf Hemmecke

SetPart::count(n) $ n=0..10

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975

Post by Ralf Hemmecke

combinat::setPartitions::count(n) $ n=0..10

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975

I guess the use of Sequence above may make the algorithms a little bit
faster as you give a hint to the program that the internal Set is
trivial w.r.t. unlabeled objects.

Cheers,
Nicolas