CombinatorialCase111 - Revision history

WikiSysop at 21:47, 21 October 2017

2017-10-21T21:47:18Z

← Older revision		Revision as of 17:47, 21 October 2017
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	* <apll>M</apll> labeled balls (1), <apll>N</apll> labeled boxes (1), any # balls per box (1)		* <apll>M</apll> labeled balls (1), <apll>N</apll> labeled boxes (1), any # balls per box (1)
	* Sensitive to <apll>⎕IO</apll>		* Sensitive to <apll>⎕IO</apll>
			* Allows Lexicographic order
	* Counted result is an integer scalar		* Counted result is an integer scalar
	* Generated result is an integer matrix.		* Generated result is an integer matrix.
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	<pre>		<pre>
	~~110~~ 1‼2 3		111 1‼2 3 ⍝ Tuples in unspecified order
	1 1		1 1
	1 2		1 2
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	3 2		3 2
	3 3		3 3
			111 2‼2 3 ⍝ Tuples in Lexicographic order
			1 1
			1 2
			1 3
			2 1
			2 2
			2 3
			3 1
			3 2
			3 3
			111 3‼2 3 ⍝ Gray Code order for Tuples not implemented as yet
			NONCE ERROR
			111 3‼2 3
			∧
	⍝ M-tuples of N items		⍝ M-tuples of N items
	⍝ Labeled balls & boxes, any # Balls per Box		⍝ Labeled balls & boxes, any # Balls per Box

WikiSysop at 22:23, 14 May 2017

2017-05-14T22:23:07Z

← Older revision		Revision as of 18:23, 14 May 2017
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	This case produces '''<apll>L</apll>-Tuples of <apll>R</apll> items'''. That is, all length <apll>L</apll> vectors with all possibilities of <apll>R</apll> items in each position, <apll>R*L</apll> rows all together.		This case produces '''<apll>M</apll>-Tuples of <apll>N</apll> items'''. That is, all length <apll>M</apll> vectors with all possibilities of <apll>N</apll> items in each position, <apll>N*M</apll> rows all together.

	* <apll>L</apll> labeled balls (1), <apll>R</apll> labeled boxes (1), any # balls per box (1)		* <apll>M</apll> labeled balls (1), <apll>N</apll> labeled boxes (1), any # balls per box (1)
	* Sensitive to <apll>⎕IO</apll>		* Sensitive to <apll>⎕IO</apll>
	* Counted result is an integer scalar		* Counted result is an integer scalar
	* Generated result is an integer matrix.		* Generated result is an integer matrix.

	The count for this function is <apll>R<sup>L</sup></apll> (<apll>↔ R*L</apll>).		The count for this function is <apll>N<sup>M</sup></apll> (<apll>↔ N*M</apll>).

	For example:		For example:
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	3 2		3 2
	3 3		3 3
	⍝ L-tuples of R items		⍝ M-tuples of N items
	⍝ Labeled balls & boxes, any # Balls per Box		⍝ Labeled balls & boxes, any # Balls per Box
	111 0‼3 2		111 0‼3 2

WikiSysop at 01:48, 30 April 2017

2017-04-30T01:48:22Z

← Older revision		Revision as of 21:48, 29 April 2017
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	This case produces <apll>L</apll>-~~'''~~Tuples~~'''~~ of <apll>R</apll> items. That is, all length <apll>L</apll> vectors with all possibilities of <apll>R</apll> items in each position, <apll>R*L</apll> rows all together.		This case produces '''<apll>L</apll>-Tuples of <apll>R</apll> items'''. That is, all length <apll>L</apll> vectors with all possibilities of <apll>R</apll> items in each position, <apll>R*L</apll> rows all together.

	* <apll>L</apll> labeled balls (1), <apll>R</apll> labeled boxes (1), any # balls per box (1)		* <apll>L</apll> labeled balls (1), <apll>R</apll> labeled boxes (1), any # balls per box (1)

WikiSysop at 01:19, 30 April 2017

2017-04-30T01:19:02Z

← Older revision		Revision as of 21:19, 29 April 2017
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	3 3		3 3
	⍝ L-tuples of R items		⍝ L-tuples of R items
	⍝ Labeled balls & boxes, any #~~bpb~~		⍝ Labeled balls & boxes, any # Balls per Box
	111 0‼3 2		111 0‼3 2
	8		8

WikiSysop: Created page with "This case produces L-'''Tuples''' of R items. That is, all length L vectors with all possibilities of R items in each posi..."

2017-04-29T22:35:28Z

Created page with "This case produces <apll>L</apll>-'''Tuples''' of <apll>R</apll> items. That is, all length <apll>L</apll> vectors with all possibilities of <apll>R</apll> items in each posi..."

New page

This case produces <apll>L</apll>-'''Tuples''' of <apll>R</apll> items. That is, all length <apll>L</apll> vectors with all possibilities of <apll>R</apll> items in each position, <apll>R*L</apll> rows all together.

* <apll>L</apll> labeled balls (1), <apll>R</apll> labeled boxes (1), any # balls per box (1)
* Sensitive to <apll>⎕IO</apll>
* Counted result is an integer scalar
* Generated result is an integer matrix.

The count for this function is <apll>RL</apll> (<apll>↔ R*L</apll>).

For example:

If we have 2 labeled balls (❶❷) and 3 labeled boxes (<apll>123</apll>) with any # of balls per box, there are <apll>9</apll> (<apll>↔ 3*2</apll>) ways to meet these criteria:

{| border="0" cellpadding="5" cellspacing="0"
|
{| border="1" cellpadding="5" cellspacing="0"
|❶ ❷
|   
|   
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|
{| border="1" cellpadding="5" cellspacing="0"
|  ❶
|  ❷
|   
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|
{| border="1" cellpadding="5" cellspacing="0"
|  ❶
|   
|  ❷
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|
{| border="1" cellpadding="5" cellspacing="0"
|  ❷
|  ❶
|   
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|
{| border="1" cellpadding="5" cellspacing="0"
|   
|❶ ❷
|   
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|
{| border="1" cellpadding="5" cellspacing="0"
|   
|  ❶
|  ❷
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|
{| border="1" cellpadding="5" cellspacing="0"
|  ❷
|   
|  ❶
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|
{| border="1" cellpadding="5" cellspacing="0"
|   
|  ❷
|  ❶
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|
{| border="1" cellpadding="5" cellspacing="0"
|   
|   
|❶ ❷
|-
|align="center"|1
|align="center"|2
|align="center"|3
|}
|}

The diagram above corresponds to

<pre>
110 1‼2 3
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
⍝ L-tuples of R items
⍝ Labeled balls & boxes, any #bpb
111 0‼3 2
8
111 1‼3 2
1 1 1
1 1 2
1 2 1
1 2 2
2 1 1
2 1 2
2 2 1
2 2 2
</pre>