K14a2082

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a2082

Polynomial invariants

Jones polynomial	Data:K14a2082/Jones Polynomial
Alexander polynomial	$-t^{5}+8t^{4}-28t^{3}+63t^{2}-100t+117-100t^{-1}+63t^{-2}-28t^{-3}+8t^{-4}-t^{-5}$
Conway polynomial	Data:K14a2082/Conway Polynomial
Determinant	Data:K14a2082/Determinant
Signature	Data:K14a2082/Signature
HOMFLY-PT polynomial	$-z^{10}+2a^{2}z^{8}+2z^{8}a^{-2}-6z^{8}-a^{4}z^{6}+10a^{2}z^{6}+10z^{6}a^{-2}-z^{6}a^{-4}-17z^{6}-4a^{4}z^{4}+21a^{2}z^{4}+20z^{4}a^{-2}-4z^{4}a^{-4}-28z^{4}-6a^{4}z^{2}+21a^{2}z^{2}+18z^{2}a^{-2}-5z^{2}a^{-4}-25z^{2}-3a^{4}+8a^{2}+6a^{-2}-2a^{-4}-8$
Kauffman polynomial	Failed to parse (syntax error): {\displaystyle 2 \text{QuantumGroups$\grave{ }$a} z^{13}+2 z^{13} $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+8 z^{12} $Failed^{-1} +16 z^{12}+14 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+30 \text{QuantumGroups$\grave{ }$a} z^{11}+29 z^{11} $Failed^{-1} +13 z^{11} $Failed^{-1} +14 \text{QuantumGroups$\grave{ }$a}^4 z^{10}+14 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+8 z^{10} $Failed^{-1} +12 z^{10} $Failed^{-1} -4 z^{10}+9 \text{QuantumGroups$\grave{ }$a}^5 z^9-19 \text{QuantumGroups$\grave{ }$a}^3 z^9-79 \text{QuantumGroups$\grave{ }$a} z^9-80 z^9 $Failed^{-1} -21 z^9 $Failed^{-1} +8 z^9 $Failed^{-1} +4 \text{QuantumGroups$\grave{ }$a}^6 z^8-30 \text{QuantumGroups$\grave{ }$a}^4 z^8-73 \text{QuantumGroups$\grave{ }$a}^2 z^8-52 z^8 $Failed^{-1} -23 z^8 $Failed^{-1} +4 z^8 $Failed^{-1} -64 z^8+\text{QuantumGroups$\grave{ }$a}^7 z^7-20 \text{QuantumGroups$\grave{ }$a}^5 z^7+87 \text{QuantumGroups$\grave{ }$a} z^7+98 z^7 $Failed^{-1} +14 z^7 $Failed^{-1} -17 z^7 $Failed^{-1} +z^7 $Failed^{-1} -10 \text{QuantumGroups$\grave{ }$a}^6 z^6+28 \text{QuantumGroups$\grave{ }$a}^4 z^6+108 \text{QuantumGroups$\grave{ }$a}^2 z^6+81 z^6 $Failed^{-1} +14 z^6 $Failed^{-1} -11 z^6 $Failed^{-1} +126 z^6-3 \text{QuantumGroups$\grave{ }$a}^7 z^5+15 \text{QuantumGroups$\grave{ }$a}^5 z^5+10 \text{QuantumGroups$\grave{ }$a}^3 z^5-55 \text{QuantumGroups$\grave{ }$a} z^5-68 z^5 $Failed^{-1} -9 z^5 $Failed^{-1} +9 z^5 $Failed^{-1} -3 z^5 $Failed^{-1} +8 \text{QuantumGroups$\grave{ }$a}^6 z^4-21 \text{QuantumGroups$\grave{ }$a}^4 z^4-92 \text{QuantumGroups$\grave{ }$a}^2 z^4-70 z^4 $Failed^{-1} -5 z^4 $Failed^{-1} +10 z^4 $Failed^{-1} -118 z^4+3 \text{QuantumGroups$\grave{ }$a}^7 z^3-5 \text{QuantumGroups$\grave{ }$a}^5 z^3-8 \text{QuantumGroups$\grave{ }$a}^3 z^3+14 \text{QuantumGroups$\grave{ }$a} z^3+21 z^3 $Failed^{-1} +5 z^3 $Failed^{-1} +z^3 $Failed^{-1} +3 z^3 $Failed^{-1} -2 \text{QuantumGroups$\grave{ }$a}^6 z^2+12 \text{QuantumGroups$\grave{ }$a}^4 z^2+42 \text{QuantumGroups$\grave{ }$a}^2 z^2+32 z^2 $Failed^{-1} +5 z^2 $Failed^{-1} -3 z^2 $Failed^{-1} +52 z^2-\text{QuantumGroups$\grave{ }$a}^7 z+\text{QuantumGroups$\grave{ }$a}^5 z+3 \text{QuantumGroups$\grave{ }$a}^3 z-2 z $Failed^{-1} -z $Failed^{-1} -z $Failed^{-1} -z $Failed^{-1} -3 \text{QuantumGroups$\grave{ }$a}^4-8 \text{QuantumGroups$\grave{ }$a}^2-6 $Failed^{-1} -2 $Failed^{-1} -8}

Modifying This Page

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