K14a1953

Knot presentations

Dowker-Thistlethwaite code

4 8 16 2 26 18 22 6 14 24 12 20 28 10

Notes on presentations of K14a1953

Polynomial invariants

Jones polynomial	Data:K14a1953/Jones Polynomial
Alexander polynomial	$-2t^{4}+16t^{3}-51t^{2}+96t-117+96t^{-1}-51t^{-2}+16t^{-3}-2t^{-4}$
Conway polynomial	Data:K14a1953/Conway Polynomial
Determinant	Data:K14a1953/Determinant
Signature	Data:K14a1953/Signature
HOMFLY-PT polynomial	$-z^{8}a^{-2}-z^{8}+a^{2}z^{6}-z^{6}a^{-2}+3z^{6}a^{-4}-3z^{6}+2a^{2}z^{4}+4z^{4}a^{-2}+7z^{4}a^{-4}-3z^{4}a^{-6}-5z^{4}+a^{2}z^{2}+10z^{2}a^{-2}+4z^{2}a^{-4}-6z^{2}a^{-6}+z^{2}a^{-8}-6z^{2}+7a^{-2}-a^{-4}-3a^{-6}+a^{-8}-3$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle z^{13} $Failed^{-1} +z^{13} $Failed^{-1} +9 z^{12} $Failed^{-1} +4 z^{12} $Failed^{-1} +5 z^{12}+10 \text{QuantumGroups$\grave{ }$a} z^{11}+22 z^{11} $Failed^{-1} +20 z^{11} $Failed^{-1} +8 z^{11} $Failed^{-1} +10 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+17 z^{10} $Failed^{-1} +23 z^{10} $Failed^{-1} +11 z^{10} $Failed^{-1} +15 z^{10}+5 \text{QuantumGroups$\grave{ }$a}^3 z^9-16 \text{QuantumGroups$\grave{ }$a} z^9-41 z^9 $Failed^{-1} -16 z^9 $Failed^{-1} +15 z^9 $Failed^{-1} +11 z^9 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4 z^8-31 \text{QuantumGroups$\grave{ }$a}^2 z^8-88 z^8 $Failed^{-1} -51 z^8 $Failed^{-1} -z^8 $Failed^{-1} +8 z^8 $Failed^{-1} -78 z^8-17 \text{QuantumGroups$\grave{ }$a}^3 z^7-25 \text{QuantumGroups$\grave{ }$a} z^7-36 z^7 $Failed^{-1} -71 z^7 $Failed^{-1} -59 z^7 $Failed^{-1} -12 z^7 $Failed^{-1} +4 z^7 $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^4 z^6+28 \text{QuantumGroups$\grave{ }$a}^2 z^6+72 z^6 $Failed^{-1} +12 z^6 $Failed^{-1} -28 z^6 $Failed^{-1} -13 z^6 $Failed^{-1} +z^6 $Failed^{-1} +77 z^6+20 \text{QuantumGroups$\grave{ }$a}^3 z^5+57 \text{QuantumGroups$\grave{ }$a} z^5+102 z^5 $Failed^{-1} +122 z^5 $Failed^{-1} +64 z^5 $Failed^{-1} -z^5 $Failed^{-1} -8 z^5 $Failed^{-1} +3 \text{QuantumGroups$\grave{ }$a}^4 z^4-6 \text{QuantumGroups$\grave{ }$a}^2 z^4-10 z^4 $Failed^{-1} +29 z^4 $Failed^{-1} +36 z^4 $Failed^{-1} +8 z^4 $Failed^{-1} -2 z^4 $Failed^{-1} -22 z^4-9 \text{QuantumGroups$\grave{ }$a}^3 z^3-35 \text{QuantumGroups$\grave{ }$a} z^3-72 z^3 $Failed^{-1} -80 z^3 $Failed^{-1} -32 z^3 $Failed^{-1} +8 z^3 $Failed^{-1} +6 z^3 $Failed^{-1} -\text{QuantumGroups$\grave{ }$a}^4 z^2-\text{QuantumGroups$\grave{ }$a}^2 z^2+2 z^2 $Failed^{-1} -15 z^2 $Failed^{-1} -17 z^2 $Failed^{-1} -3 z^2 $Failed^{-1} +z^2 $Failed^{-1} +4 z^2+\text{QuantumGroups$\grave{ }$a}^3 z+9 \text{QuantumGroups$\grave{ }$a} z+21 z $Failed^{-1} +23 z $Failed^{-1} +8 z $Failed^{-1} -4 z $Failed^{-1} -2 z $Failed^{-1} -7 $Failed^{-1} - $Failed^{-1} +3 $Failed^{-1} + $Failed^{-1} -3}

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Large Knot Page master template. Back to the top.