K14a14222

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K14a14222

Polynomial invariants

Jones polynomial	Data:K14a14222/Jones Polynomial
Alexander polynomial	$-t^{5}+9t^{4}-32t^{3}+66t^{2}-93t+103-93t^{-1}+66t^{-2}-32t^{-3}+9t^{-4}-t^{-5}$
Conway polynomial	Data:K14a14222/Conway Polynomial
Determinant	Data:K14a14222/Determinant
Signature	Data:K14a14222/Signature
HOMFLY-PT polynomial	$-a^{4}z^{10}+2a^{6}z^{8}-5a^{4}z^{8}+2a^{2}z^{8}-a^{8}z^{6}+9a^{6}z^{6}-10a^{4}z^{6}+8a^{2}z^{6}-z^{6}-4a^{8}z^{4}+14a^{6}z^{4}-13a^{4}z^{4}+10a^{2}z^{4}-3z^{4}-4a^{8}z^{2}+12a^{6}z^{2}-11a^{4}z^{2}+7a^{2}z^{2}-2z^{2}-2a^{8}+5a^{6}-5a^{4}+3a^{2}$
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 z^5 \text{QuantumGroups$\grave{ }$a}^{13}-z^3 \text{QuantumGroups$\grave{ }$a}^{13}+4 z^6 \text{QuantumGroups$\grave{ }$a}^{12}-3 z^4 \text{QuantumGroups$\grave{ }$a}^{12}+10 z^7 \text{QuantumGroups$\grave{ }$a}^{11}-10 z^5 \text{QuantumGroups$\grave{ }$a}^{11}+5 z^3 \text{QuantumGroups$\grave{ }$a}^{11}-z \text{QuantumGroups$\grave{ }$a}^{11}+19 z^8 \text{QuantumGroups$\grave{ }$a}^{10}-28 z^6 \text{QuantumGroups$\grave{ }$a}^{10}+20 z^4 \text{QuantumGroups$\grave{ }$a}^{10}-3 z^2 \text{QuantumGroups$\grave{ }$a}^{10}+28 z^9 \text{QuantumGroups$\grave{ }$a}^9-52 z^7 \text{QuantumGroups$\grave{ }$a}^9+38 z^5 \text{QuantumGroups$\grave{ }$a}^9-7 z^3 \text{QuantumGroups$\grave{ }$a}^9+z \text{QuantumGroups$\grave{ }$a}^9+33 z^{10} \text{QuantumGroups$\grave{ }$a}^8-74 z^8 \text{QuantumGroups$\grave{ }$a}^8+67 z^6 \text{QuantumGroups$\grave{ }$a}^8-38 z^4 \text{QuantumGroups$\grave{ }$a}^8+14 z^2 \text{QuantumGroups$\grave{ }$a}^8-2 \text{QuantumGroups$\grave{ }$a}^8+29 z^{11} \text{QuantumGroups$\grave{ }$a}^7-63 z^9 \text{QuantumGroups$\grave{ }$a}^7+39 z^7 \text{QuantumGroups$\grave{ }$a}^7-13 z^5 \text{QuantumGroups$\grave{ }$a}^7-3 z^3 \text{QuantumGroups$\grave{ }$a}^7+2 z \text{QuantumGroups$\grave{ }$a}^7+16 z^{12} \text{QuantumGroups$\grave{ }$a}^6-5 z^{10} \text{QuantumGroups$\grave{ }$a}^6-98 z^8 \text{QuantumGroups$\grave{ }$a}^6+158 z^6 \text{QuantumGroups$\grave{ }$a}^6-118 z^4 \text{QuantumGroups$\grave{ }$a}^6+39 z^2 \text{QuantumGroups$\grave{ }$a}^6-5 \text{QuantumGroups$\grave{ }$a}^6+4 z^{13} \text{QuantumGroups$\grave{ }$a}^5+38 z^{11} \text{QuantumGroups$\grave{ }$a}^5-165 z^9 \text{QuantumGroups$\grave{ }$a}^5+202 z^7 \text{QuantumGroups$\grave{ }$a}^5-112 z^5 \text{QuantumGroups$\grave{ }$a}^5+25 z^3 \text{QuantumGroups$\grave{ }$a}^5-z \text{QuantumGroups$\grave{ }$a}^5+26 z^{12} \text{QuantumGroups$\grave{ }$a}^4-65 z^{10} \text{QuantumGroups$\grave{ }$a}^4-7 z^8 \text{QuantumGroups$\grave{ }$a}^4+103 z^6 \text{QuantumGroups$\grave{ }$a}^4-86 z^4 \text{QuantumGroups$\grave{ }$a}^4+34 z^2 \text{QuantumGroups$\grave{ }$a}^4-5 \text{QuantumGroups$\grave{ }$a}^4+4 z^{13} \text{QuantumGroups$\grave{ }$a}^3+19 z^{11} \text{QuantumGroups$\grave{ }$a}^3-112 z^9 \text{QuantumGroups$\grave{ }$a}^3+144 z^7 \text{QuantumGroups$\grave{ }$a}^3-61 z^5 \text{QuantumGroups$\grave{ }$a}^3+11 z^3 \text{QuantumGroups$\grave{ }$a}^3+10 z^{12} \text{QuantumGroups$\grave{ }$a}^2-22 z^{10} \text{QuantumGroups$\grave{ }$a}^2-23 z^8 \text{QuantumGroups$\grave{ }$a}^2+76 z^6 \text{QuantumGroups$\grave{ }$a}^2-50 z^4 \text{QuantumGroups$\grave{ }$a}^2+17 z^2 \text{QuantumGroups$\grave{ }$a}^2-3 \text{QuantumGroups$\grave{ }$a}^2+10 z^{11} \text{QuantumGroups$\grave{ }$a}-37 z^9 \text{QuantumGroups$\grave{ }$a}+39 z^7 \text{QuantumGroups$\grave{ }$a}-5 z^5 \text{QuantumGroups$\grave{ }$a}-8 z^3 \text{QuantumGroups$\grave{ }$a}+2 z \text{QuantumGroups$\grave{ }$a}+5 z^{10}-21 z^8+32 z^6-21 z^4+5 z^2+z^9 $Failed^{-1} -4 z^7 $Failed^{-1} +6 z^5 $Failed^{-1} -4 z^3 $Failed^{-1} +z $Failed^{-1} }

Modifying This Page

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