3 possible bugs in last development build

[teoman]

No argue about this, i guess Teoman interpreted permutations well as all possible changes of place with 5 different numbers. And all that combinations are still the same draw.

I´ve checked the definition about Permutations in Wiki, and it says that "in In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging in an ordered fashion) objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. For example, there are six permutations of the set {1,2,3}, namely [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], and [3,2,1]. One might define an anagram of a word as a permutation of its letters. The study of permutations in this sense generally belongs to the field of combinatorics.

So i guess i´m addressing to a particular case of permutations... . I´m adressing permutations not of the numbers themselves, but of their structure, their group (their symmetric group to be more exact).
In this sense, 1, 3, 5, 7, 9 is the same as 2, 4, 6, 8, 10 (the subjacent group is that the diferences between all of them is 2, or 2-2-2-2, or "adjacents" +2).

In some of my previous posts, conscient of this confusion i tried to use also the term "Transformation". Wether it should be called Permutations Builder is in fact dubious, as Teoman posted, specially for those that have some mathematic notion, maybe Stan as a better idea.

Best regards,

F.

Permutation refers only to a specific group of numbers (1, 2, 3, 4, 5) and each sequence of the 120 (1 * 2 * 3 * 4 * 5 = 120) contains each number only once, every number will be on position by 1 * 2 * 3 * 4 = 24 times. The number of permutations is known as 'n!' (factorial). There are three ways of ordering the numbers: arrangements, permutations and combinations.

[stan]

i think the new feature should be called 'transformations' (permutations are subset of transformations). each pool number would transform into a set of other numbers (and the set can be empty). the sets of transformed numbers may naturally overlap. filter will then accept a ticket if it contains specified count of transformed numbers.

[Gatsby]

Hi Stan,

That seems ok, but please mind that

"each pool number would transform into a set of other numbers (and the set can be empty)."

I guess you mean each pool number transform into a another number (this will became the rule). Then the last combination is transformed according to this rule (or a range of combinations) and the result transformed combination is used as a filter.

"the sets of transformed numbers may naturally overlap"

Yes, because according to the rule established some numbers can overlap.

"filter will then accept a ticket if it contains specified count of transformed numbers"

Yes. For each rule of transformation there will be a combination (or a set of combinations if someone chooses to transform a range of draws) from which we will filter. More or less as creating number groups. I think the interface should allow the creation of the rule of transformation, the atribution of a name and the hability to be applied as a single filter, that is, after creating each rule of transformation with it´s particular settings we only would have to invoke "Transformations" without having to create a filter "transformations" for each rule. Is this possible?

"Transformations" would contain groups of "Transformations of the same group"* which in turn would contain several "rules of transformation"
To apply the filter we would invoke this groups*

Example:

~Transformations:

Group 1"Transformations to adjacent movement"
rules 1) all numbers in pool number are transformed by movement by +1 (that is, 1 transforms to 2, 2 transforms to 3 ... changing evens with pairs..
rule 2) all numbers in number pool are transforme according to movement by +2
...

Group 2 "Transformations in which 1, 10, 20, 30, 40 and 50 don´t change"
rule 1) numbers in number pool are transforme as 1 transforms to 1, 2 transforms into 12,
etc

Inside Transformations we must have the possibility to create a new group of transformations, and inside the new group, the number of rules

If this is not possible at least it should allow to create as many rules (using for each a board as with swapp numbers) as we want inside the group of Transformations, each with it´s own name: as "movement by +1", "movement by +2", movement by +3" ... , all to be applied in the same step.

Thanks.