Add `first...()`, `next...()` and `islast...()` for `setparts()` and `multinomial()`

RobinHankin / partitions

R package for integer partitions

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Add `first...()`, `next...()` and `islast...()` for `setparts()` and `multinomial()` #34

Open jassler opened 1 year ago

jassler commented 1 year ago

I saw that for most partition enumeration functions, there is an equivalent next...() function.

Matrix function	first function	next function	is last function
`parts()`	`firstpart()`	`nextpart()`	`islastpart()`
`diffparts()`	`firstdiffpart()`	`nextdiffpart()`	`islastdiffpart()`
`restrictedparts()`	`firstrestrictedpart()`	`nextrestrictedpart()`	`islastrestrictedpart()`
`blockparts()`	`firstblockpart()`	`nextblockpart()`	`islastblockpart()`
`compositions()`	`firstcomposition()`	`nextcomposition()`	`islastcomposition()`
`setparts()`
`multinomial()`

Is it possible to add these generative functions for setparts() and multinomial() as well?

jassler commented 1 year ago

Additionaly, without knowing too much about these algorithms, is it possible to generate them in reverse order? I.e., introduce lastpart(), prevpart() and isfirstpart() functions, for example.

RobinHankin commented 1 year ago

jassler, you make some excellent suggestions. The short answer is that I am not sure whether they are easy or even possible to implement. Do you have a use-case I could think about? The package isn't under active development right now, but I do work on it occasionally.

Best wishes, Robin

jassler commented 1 year ago

Hey, thanks for your reply! I am working on my package socialranking and tried to work on a way to generate all possible total preorders given a set of elements (I'm using a combination of compositions() and multinomial(), see here if you're interested).

At around ~21 elements, compositions() becomes too unwieldy. Granted - in my context it's also way too unpractical to use. But, if there's a way to keep it light using something like nextcomposition(), I'd love to offer the light option as well :)

jassler commented 1 year ago

Ah, and for the reverse part, I have the following example from the function I linked to:

#' # (ab ~ a ~ b)
#' # (ab ~ a) > b
#' # (ab ~ b) > a
#' # (a ~ b) > ab
#' # ab > (a ~ b)
#' # a > (ab ~ b)
#' # b > (ab ~ a)
#' # ab > a > b
#' # ab > b > a
#' # a > ab > b
#' # b > ab > a
#' # a > b > ab
#' # b > a > ab

I offer the option to start with linear orders, which is basically just reversing the partitions, or, reversing the order of multinomial(). This should produce the following.

#' # ab > a > b
#' # ab > b > a
#' # a > ab > b
#' # b > ab > a
#' # a > b > ab
#' # b > a > ab
#' # ab > (a ~ b)
#' # a > (ab ~ b)
#' # b > (ab ~ a)
#' # (ab ~ a) > b
#' # (ab ~ b) > a
#' # (a ~ b) > ab
#' # (ab ~ a ~ b)