<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>

<Text-field style="Heading 1" layout="Heading 1">Background to Subdivisions of a Multiset</Text-field>

<Text-field style="Heading 2" layout="Heading 2"> Consruction of set partitions</Text-field>

List all partitions of a set. The parameter "N" indicates the number of blocks in which the set is subdivided.

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

Example

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

Nic8IzwlJkkmYWxwaGFHNiI2IyIiIiZGJjYjIiIjJkYmNiMiIiQ8JDwjRi08JEYlRio8JDwjRiU8JEYqRi08JDwjRio8JEYlRi08JUY0RjdGMQ==

<Text-field style="Heading 2" layout="Heading 2"> Subdivision of a special multiset: <Equation executable="false" style="2D Comment" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJNRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkobWZlbmNlZEdGJDYmLUYjNiQtSSVtc3VwR0YkNiUtRiw2JVEoJmFscGhhO0YnL0Y1RkJGPi1GLDYlUSQoaSlGJ0Y0RjcvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj5GPi8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRidGPkYrRj4=">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</Equation></Text-field>

When the multiset has support equal to a {LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg==}, the output is the follow:

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

NyUvJkkmYWxwaGFHNiI2IyIiIkYlLyZGJTYjIiIjRiUvJkYlNiMiIiRGJQ==

Nic3IyooJkkmYWxwaGFHNiI2IyIiIkYpJkYmNiMiIiNGKSZGJjYjIiIkRik3JEYtKiZGJUYpRipGKTckRiUqJkYqRilGLUYpNyRGKiomRiVGKUYtRik3JUYlRipGLQ==

L0krUGFydGl0aW9uc0c2IjcnNyMqJClJJmFscGhhR0YkIiIkIiIiNyRGKSokKUYpIiIjRitGLEYsNyVGKUYpRik=

The output can be compacted by using the following notation where the subdivisions appear togeter with their multiplicity:

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.

The above print-out is the output of the following routine:

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

Example

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

NyU3JDclSSZhbHBoYUc2IkYlRiUiIiI3JDckRiUqJClGJSIiI0YnIiIkNyQ3IyokKUYlRi1GJ0Yn

<Text-field style="Heading 1" layout="Heading 1">Subdivisions of a multiset</Text-field>

When in the multiset there are two or more different elements, the result is different from the previous one. Also in this case we use integer partitions for constructing subdivisions. This device reduces the computational complexity. The list of all partitions of a set with 3 blocks is:

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,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, 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 , 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, 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.

Setting 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 we obtain:

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

Compacting the previous output we obtain:

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

<Text-field style="Heading 2" layout="Heading 2">The Maple routines</Text-field>

<Text-field style="Text" size="14" bold="true" family="Serif" layout="Heading 3"> Some details on secondary Maple routines</Text-field>

The following function calcules the product of factorials of multiplicity.

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

Example

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

IiM3

The following function inserts an element into an array with the following rules:

1) the element must not be in a previous block with the same or less degree

2) jump every block equal to the previous

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

Examples

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

NiQ3JSomSSJhRzYiIiIiSSJiR0YmRidGJUYlNyZGJUYlRiVGKA==

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

NiQ3JkkiYUc2IkYkSSJiR0YlKiZGJCIiIkYmRig3J0YkRiRGJkYkRiY=

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

NydJImFHNiJGI0YjSSJiR0YkRiU=

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

NydJImFHNiJGI0YjKiQpSSJiR0YkIiIjIiIiRic=

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

NiQ3JiomSSJhRzYiIiIiKUkiYkdGJiIiI0YnRiVGJUYpNydGJUYlRiVGKSokRihGJw==

JSFH

The following function inserts more then one elements into an array with the same rules.

Note: the array contains also the multeplicity of the multiset

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

Examples

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

NiU3JDclKiZJImFHNiIiIiJJImJHRidGKEYlRiZGKDckNyZGJUYmRiZGKUYoNyQ3J0YmRiZGJkYpRilGKA==

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

NiU3JDclKiZJImFHNiIiIiJJImJHRidGKEYlRiYiIic3JDcmRiVGJkYmRilGKjckNydGJkYmRiZGKUYpRio=

The following function is an extension of previous one. The input can be more then two vectors.

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

Examples

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

Nig3JDckKihJImFHNiIiIiJJImJHRidGKEkiY0dGJ0YoRiYiIiM3JDckKiZGJkYoRilGKComRiZGKEYqRihGKzckNyVGLkYmRipGKzckNyVGL0YmRilGKzckNyVGJkYmKiZGKUYoRipGKEYoNyQ3JkYmRiZGKUYqRig=

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

Niw3JDclKihJImFHNiIiIiJJImJHRidGKEkiY0dGJ0YoKiZGJkYoRilGKEYmIiM3NyQ3JUYrRisqJkYmRihGKkYoIiInNyQ3JkYrRitGJkYqRjA3JDcmRiVGJkYmRilGMDckNyZGK0YvRiZGKUYsNyQ3JkYrRiZGJiomRilGKEYqRihGMDckNydGK0YmRiZGKUYqRjA3JDcnRi9GJkYmRilGKSIiJDckNydGJkYmRiZGOUYpIiIjNyQ3KEYmRiZGJkYpRilGKkYo

The following function makes the Cartesian Product.

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

Examples

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

Nig3JEkiWEc2IkkmYWxwaGFHRiU3JEYkSSViZXRhR0YlNyRGJEkmZ2FtbWFHJSpwcm90ZWN0ZWRHNyRJIllHRiVGJjckRi1GKDckRi1GKg==

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

Nio3JUkiWEc2IkkmYWxwaGFHRiVJInJHRiU3JUYkRiZJInNHRiU3JUYkSSViZXRhR0YlRic3JUYkRitGKTclSSJZR0YlRiZGJzclRi5GJkYpNyVGLkYrRic3JUYuRitGKQ==

<Text-field style="Text" size="14" bold="true" family="Serif" layout="Heading 3"> The master function</Text-field>

A Maple algorithm for listing multisets subdivisions.

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

Examples

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

Nyc3JDcmJkkmYWxwaGFHNiI2IyIiIkYlRiVGJUYpNyQ3JUYlRiUqJClGJSIiI0YpIiInNyQ3JEYsRiwiIiQ3JDckRiUqJClGJUYyRikiIiU3JDcjKiQpRiVGN0YpRik=

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

Nys3JDckKiYmSSZhbHBoYUc2IjYjIiIiRiomRic2IyIiI0YqRiVGLTckNyVGJUYmRisiIiU3JDcmRiZGJkYrRitGKjckNyQqJkYmRiopRitGLUYqRiZGLTckNyVGJkYmKiRGNkYqRio3JDckKiYpRiZGLUYqRitGKkYrRi03JDclKiRGPUYqRitGK0YqNyQ3IyomRj1GKkY2RipGKjckNyRGQEY5Rio=

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

Ny03JDckKigmSSZhbHBoYUc2IjYjIiIiRiomRic2IyIiI0YqJkYnNiMiIiRGKkYmRi03JDckKiZGJkYqRitGKiomRiZGKkYuRipGLTckNyVGM0YmRi5GLTckNyVGNEYmRitGLTckNyVGJkYmKiZGK0YqRi5GKkYqNyQ3JkYmRiZGK0YuRio3JDcjKigpRiZGLUYqRitGKkYuRipGKjckNyQqJkZBRipGK0YqRi5GKjckNyQqJkZBRipGLkYqRitGKjckNyQqJEZBRipGO0YqNyQ3JUZKRitGLkYq

Note: the notion of subdivision as been introduced in [2].

In the subdivision list, the sum of all multiplicity is the Bell Number.

Moreover the same multiplicities of the subdivision with the same block numbers is the Stirling Number of the second kind.

Example: from "makeTab(4)" we obtain:

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

in wich it is possible to observe:

1 = combinat['stirling2'](4,4) =combinat['stirling2'](4,1);

6 = combinat['stirling2'](4,3);

3 + 4 = 7 = combinat['stirling2'](4,2);

and 1 + 6 + 3 + 4 + 1 = 15 = combinat['Bell'](4).