Partitions of (\mathcal S_1)

<tr>
    <td>\([1]\)</td>
    <td>\([1]\)</td>
    <td><pre>#</pre></td>
    <td>\((\cdot)\)</td>
    <td>\(+\)</td>
    <td>(1)</td>
    <td>1</td>
</tr>
Long form Short form Young frame Pertinent cycle structure Parity Conjugacy classes to \(\mathcal A_1\) Number of elements in conjugacy class

Partitions of \(\mathcal S_2\)

<tr>
    <td>\([2, 0]\)</td>
    <td>\([2]\)</td>
    <td><pre>##</pre></td>
    <td>\((\cdot)(\cdot)\)</td>
    <td>\(+\)</td>
    <td>(1)(2)</td>
    <td>1</td>
</tr>

<tr>
    <td>\([1, 1]\)</td>
    <td>\([1^2]\)</td>
    <td><pre>#

#

Long form Short form Young frame Pertinent cycle structure Parity Conjugacy classes to \(\mathcal A_2\) Number of elements in conjugacy class
((\cdot\cdot)) (-) (12) 1

Partitions of \(\mathcal S_3\)

<tr>
    <td>\([3, 0, 0]\)</td>
    <td>\([3]\)</td>
    <td><pre>###</pre></td>
    <td>\((\cdot)(\cdot)(\cdot)\)</td>
    <td>\(+\)</td>
    <td>(1)(2)(3)</td>
    <td>1</td>
</tr>

<tr>
    <td>\([2, 1, 0]\)</td>
    <td>\([2, 1]\)</td>
    <td><pre>##

# 

<tr>
    <td>\([1, 1, 1]\)</td>
    <td>\([1^3]\)</td>
    <td><pre>#

#

Long form Short form Young frame Pertinent cycle structure Parity Conjugacy classes to \(\mathcal A_3\) Number of elements in conjugacy class
((\cdot\cdot)(\cdot)) (-) (12)(3)
(13)(2)
(23)(1)		 3
((\cdot\cdot\cdot)) (+) (123)
(132)		 2

Partitions of \(\mathcal S_4\)

<tr>
    <td>\([4, 0, 0, 0]\)</td>
    <td>\([4]\)</td>
    <td><pre>####</pre></td>
    <td>\((\cdot)(\cdot)(\cdot)(\cdot)\)</td>
    <td>\(+\)</td>
    <td>(1)(2)(3)(4)</td>
    <td>1</td>
</tr>

<tr>
    <td>\([3, 1, 0, 0]\)</td>
    <td>\([3, 1]\)</td>
    <td><pre>###

# 

<tr>
    <td>\([2, 2, 0, 0]\)</td>
    <td>\([2^2]\)</td>
    <td><pre>##

## 

<tr>
    <td>\([2, 1, 1, 0]\)</td>
    <td>\([2, 1^2]\)</td>
    <td><pre>##

# 

<tr>
    <td>\([1, 1, 1, 1]\)</td>
    <td>\([1^4]\)</td>
    <td><pre>#

#

Long form Short form Young frame Pertinent cycle structure Parity Conjugacy classes to \(\mathcal A_4\) Number of elements in conjugacy class
((\cdot\cdot)(\cdot)(\cdot)) (-) (12)(3)(4)
(13)(2)(4)
(14)(2)(3)
(23)(1)(4)
(24)(1)(3)
(34)(1)(2)		 6
((\cdot\cdot)(\cdot\cdot)) (+) (12)(34)
(13)(24)
(14)(23)		 3
((\cdot\cdot\cdot)(\cdot)) (+) (123)(4)
(124)(3)
(132)(4)
(134)(2)
(142)(3)
(143)(2)
(234)(1)
(243)(1)		 8
((\cdot\cdot\cdot\cdot)) (-) (1234)
(1243)
(1324)
(1342)
(1423)
(1432)		 6

Partitions of \(\mathcal S_5\)

<tr>
    <td>\([5, 0, 0, 0, 0]\)</td>
    <td>\([5]\)</td>
    <td><pre>#####</pre></td>
    <td>\((\cdot)(\cdot)(\cdot)(\cdot)(\cdot)\)</td>
    <td>\(+\)</td>
    <td>(1)(2)(3)(4)(5)</td>
    <td>1</td>
</tr>

<tr>
    <td>\([4, 1, 0, 0, 0]\)</td>
    <td>\([4, 1]\)</td>
    <td><pre>####

# 

<tr>
    <td>\([3, 2, 0, 0, 0]\)</td>
    <td>\([3, 2]\)</td>
    <td><pre>###

## 

<tr>
    <td>\([3, 1, 1, 0, 0]\)</td>
    <td>\([3, 1^2]\)</td>
    <td><pre>###

# 

<tr>
    <td>\([2, 2, 1, 0, 0]\)</td>
    <td>\([2^2, 1]\)</td>
    <td><pre>##

# 

<tr>
    <td>\([2, 1, 1, 1, 0]\)</td>
    <td>\([2, 1^3]\)</td>
    <td><pre>##

# 

<tr>
    <td>\([1, 1, 1, 1, 1]\)</td>
    <td>\([1^5]\)</td>
    <td><pre>#

#

Long form Short form Young frame Pertinent cycle structure Parity Conjugacy classes to \(\mathcal A_5\) Number of elements in conjugacy class
((\cdot\cdot)(\cdot)(\cdot)(\cdot)) (-) (12)(3)(4)(5)
(13)(2)(4)(5)
(14)(2)(3)(5)
(15)(2)(3)(4)
(23)(1)(4)(5)
(24)(1)(3)(5)
(25)(1)(3)(4)
(34)(1)(2)(5)
(35)(1)(2)(4)
(45)(1)(2)(3)		 10
((\cdot\cdot)(\cdot\cdot)(\cdot)) (+) (12)(34)(5)
(12)(35)(4)
(12)(45)(3)
(13)(24)(5)
(13)(25)(4)
(13)(45)(2)
(14)(23)(5)
(14)(25)(3)
(14)(35)(2)
(15)(23)(4)
(15)(24)(3)
(15)(34)(2)
(23)(45)(1)
(24)(35)(1)
(25)(34)(1)		 15
((\cdot\cdot\cdot)(\cdot)(\cdot)) (+) (123)(4)(5)
(124)(3)(5)
(125)(3)(4)
(132)(4)(5)
(134)(2)(5)
(135)(2)(4)
(142)(3)(5)
(143)(2)(5)
(145)(2)(3)
(152)(3)(4)
(153)(2)(4)
(154)(2)(3)
(234)(1)(5)
(235)(1)(4)
(243)(1)(5)
(245)(1)(3)
(253)(1)(4)
(254)(1)(3)
(345)(1)(2)
(354)(1)(2)		 20
((\cdot\cdot\cdot)(\cdot\cdot)) (-) (123)(45)
(124)(35)
(125)(34)
(132)(45)
(134)(25)
(135)(24)
(142)(35)
(143)(25)
(145)(23)
(152)(34)
(153)(24)
(154)(23)
(234)(15)
(235)(14)
(243)(15)
(245)(13)
(253)(14)
(254)(13)
(345)(12)
(354)(12)		 20
((\cdot\cdot\cdot\cdot)(\cdot)) (-) (1234)(5)
(1235)(4)
(1243)(5)
(1245)(3)
(1253)(4)
(1254)(3)
(1324)(5)
(1325)(4)
(1342)(5)
(1345)(2)
(1352)(4)
(1354)(2)
(1423)(5)
(1425)(3)
(1432)(5)
(1435)(2)
(1452)(3)
(1453)(2)
(1523)(4)
(1524)(3)
(1532)(4)
(1534)(2)
(1542)(3)
(1543)(2)
(2345)(1)
(2354)(1)
(2435)(1)
(2453)(1)
(2534)(1)
(2543)(1)		 30
((\cdot\cdot\cdot\cdot\cdot)) (+) (12345)
(12354)
(12435)
(12453)
(12534)
(12543)
(13245)
(13254)
(13425)
(13452)
(13524)
(13542)
(14235)
(14253)
(14325)
(14352)
(14523)
(14532)
(15234)
(15243)
(15324)
(15342)
(15423)
(15432)		 24