K14a13117

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a13117

Polynomial invariants

Jones polynomial	Data:K14a13117/Jones Polynomial
Alexander polynomial	$t^{5}-9t^{4}+36t^{3}-87t^{2}+143t-167+143t^{-1}-87t^{-2}+36t^{-3}-9t^{-4}+t^{-5}$
Conway polynomial	Data:K14a13117/Conway Polynomial
Determinant	Data:K14a13117/Determinant
Signature	Data:K14a13117/Signature
HOMFLY-PT polynomial	$a^{2}z^{10}-2a^{4}z^{8}+5a^{2}z^{8}-2z^{8}+a^{6}z^{6}-7a^{4}z^{6}+11a^{2}z^{6}+z^{6}a^{-2}-7z^{6}+2a^{6}z^{4}-8a^{4}z^{4}+10a^{2}z^{4}+2z^{4}a^{-2}-7z^{4}+a^{6}z^{2}-2a^{4}z^{2}+z^{2}+a^{4}-3a^{2}-a^{-2}+4$
Kauffman polynomial	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 \text{QuantumGroups$\grave{ }$a}^3 z^{13}+4 \text{QuantumGroups$\grave{ }$a} z^{13}+18 \text{QuantumGroups$\grave{ }$a}^4 z^{12}+32 \text{QuantumGroups$\grave{ }$a}^2 z^{12}+14 z^{12}+36 \text{QuantumGroups$\grave{ }$a}^5 z^{11}+66 \text{QuantumGroups$\grave{ }$a}^3 z^{11}+50 \text{QuantumGroups$\grave{ }$a} z^{11}+20 z^{11} $Failed^{-1} +43 \text{QuantumGroups$\grave{ }$a}^6 z^{10}+41 \text{QuantumGroups$\grave{ }$a}^4 z^{10}-12 \text{QuantumGroups$\grave{ }$a}^2 z^{10}+15 z^{10} $Failed^{-1} +5 z^{10}+34 \text{QuantumGroups$\grave{ }$a}^7 z^9-29 \text{QuantumGroups$\grave{ }$a}^5 z^9-164 \text{QuantumGroups$\grave{ }$a}^3 z^9-153 \text{QuantumGroups$\grave{ }$a} z^9-46 z^9 $Failed^{-1} +6 z^9 $Failed^{-1} +18 \text{QuantumGroups$\grave{ }$a}^8 z^8-66 \text{QuantumGroups$\grave{ }$a}^6 z^8-170 \text{QuantumGroups$\grave{ }$a}^4 z^8-143 \text{QuantumGroups$\grave{ }$a}^2 z^8-43 z^8 $Failed^{-1} +z^8 $Failed^{-1} -101 z^8+6 \text{QuantumGroups$\grave{ }$a}^9 z^7-50 \text{QuantumGroups$\grave{ }$a}^7 z^7-41 \text{QuantumGroups$\grave{ }$a}^5 z^7+106 \text{QuantumGroups$\grave{ }$a}^3 z^7+129 \text{QuantumGroups$\grave{ }$a} z^7+22 z^7 $Failed^{-1} -16 z^7 $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^{10} z^6-19 \text{QuantumGroups$\grave{ }$a}^8 z^6+34 \text{QuantumGroups$\grave{ }$a}^6 z^6+161 \text{QuantumGroups$\grave{ }$a}^4 z^6+195 \text{QuantumGroups$\grave{ }$a}^2 z^6+41 z^6 $Failed^{-1} -2 z^6 $Failed^{-1} +131 z^6-3 \text{QuantumGroups$\grave{ }$a}^9 z^5+27 \text{QuantumGroups$\grave{ }$a}^7 z^5+41 \text{QuantumGroups$\grave{ }$a}^5 z^5-19 \text{QuantumGroups$\grave{ }$a}^3 z^5-36 \text{QuantumGroups$\grave{ }$a} z^5+7 z^5 $Failed^{-1} +13 z^5 $Failed^{-1} +6 \text{QuantumGroups$\grave{ }$a}^8 z^4-13 \text{QuantumGroups$\grave{ }$a}^6 z^4-66 \text{QuantumGroups$\grave{ }$a}^4 z^4-87 \text{QuantumGroups$\grave{ }$a}^2 z^4-14 z^4 $Failed^{-1} +z^4 $Failed^{-1} -55 z^4-6 \text{QuantumGroups$\grave{ }$a}^7 z^3-6 \text{QuantumGroups$\grave{ }$a}^5 z^3+7 \text{QuantumGroups$\grave{ }$a}^3 z^3+9 \text{QuantumGroups$\grave{ }$a} z^3-2 z^3 $Failed^{-1} +5 \text{QuantumGroups$\grave{ }$a}^6 z^2+11 \text{QuantumGroups$\grave{ }$a}^4 z^2+8 \text{QuantumGroups$\grave{ }$a}^2 z^2+2 z^2-2 \text{QuantumGroups$\grave{ }$a}^5 z-5 \text{QuantumGroups$\grave{ }$a}^3 z-5 \text{QuantumGroups$\grave{ }$a} z-3 z $Failed^{-1} -z $Failed^{-1} +\text{QuantumGroups$\grave{ }$a}^4+3 \text{QuantumGroups$\grave{ }$a}^2+ $Failed^{-1} +4}

Modifying This Page

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