The Multivariable Alexander Polynomial: Difference between revisions
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out= <nowiki>MultivariableAlexander[L][t] returns the multivariable Alexander polynomial of a link L as a function of the variable t[1], t[2], ..., t[c], where c is the number of components of L.</nowiki> | |
out= <nowiki>MultivariableAlexander[L][t] returns the multivariable Alexander polynomial of a link L as a function of the variable t[1], t[2], ..., t[c], where c is the number of components of L.</nowiki> | |
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about= <nowiki>The multivariable Alexander program was written by Dan Carney at the University of Toronto in the summer of 2005.</nowiki>}} |
about= <nowiki>The multivariable Alexander program was written by Dan Carney at the University of Toronto in the summer of 2005.</nowiki>}} |
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The link [[L8a21]] is symmetric under cyclic permutations of its components but not under interchanging two adjacent components. It is amusing to see how this is reflected in its multivariable Alexander polynomial: |
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<!--$$mva = MultivariableAlexander[Link[8, Alternating, 21]] /. { |
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t[1] -> t1, t[2] -> t2, t[3] -> t3, t[4] -> t4 |
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}$$--> |
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<!--$$mva - (mva /. {t1->t2, t2->t3, t3->t4, t4->t1})$$--> |
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<!--$$mva - (mva /. {t1->t2, t2->t1})$$--> |
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Revision as of 14:44, 5 September 2005
(For In[1] see Setup)
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The link L8a21 is symmetric under cyclic permutations of its components but not under interchanging two adjacent components. It is amusing to see how this is reflected in its multivariable Alexander polynomial:
There are 11 links with up to 11 crossings whose multivariable Alexander polynomial is . Here they are:
In[4]:=
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Select[AllLinks[], (MultivariableAlexander[#][t] == 0) &]
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Out[4]=
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{Link[9, NonAlternating, 27], Link[10, NonAlternating, 32],
Link[10, NonAlternating, 36], Link[10, NonAlternating, 107],
Link[11, NonAlternating, 244], Link[11, NonAlternating, 247],
Link[11, NonAlternating, 334], Link[11, NonAlternating, 381],
Link[11, NonAlternating, 396], Link[11, NonAlternating, 404],
Link[11, NonAlternating, 406]}
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