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    Perko Pair

    Notations

    Alexander-Briggs notation | 10_161 Conway notation | 3:-20:-20 Dowker notation | 4 12 -16 14 -18 2 8 -20 -10 -6

    Braid representation

    braid word | σ_1^(-1)σ_2σ_1^2σ_2^3σ_1^2σ_2 braid index | 3 braid diagram |

    Knot invariants

    crossing number | 10 unknotting number | 3 determinant | 5 signature | -4 coloring number set | {5} genus of complement | 3 Seifert matrix | (-1 | 0 | 0 | 0 | 0 | 0 0 | -1 | 0 | 0 | 0 | 0 -1 | 1 | -1 | -1 | 0 | 0 -1 | 0 | 0 | -1 | 0 | 0 -1 | 0 | 0 | -1 | -1 | 0 -1 | 1 | 0 | -1 | -1 | -1)

    Polynomial invariants

    Alexander polynomial | x^3 + 1/x^3 - 2 x - 2/x + 3 BLM/Ho polynomial | 2 x^6 + 2 x^5 - 10 x^4 - 8 x^3 + 12 x^2 + 6 x - 3 bracket polynomial | -1/x^44 + 1/x^40 - 1/x^36 + 1/x^32 - 1/x^28 + 1/x^24 + 1/x^12 Conway polynomial | x^6 + 6 x^4 + 7 x^2 + 1 HOMFLY polynomial | x^10 (-y^2) - x^10 - x^8 y^2 - x^8 + x^6 y^6 + 6 x^6 y^4 + 9 x^6 y^2 + 3 x^6 Jones polynomial | -1/x^11 + 1/x^10 - 1/x^9 + 1/x^8 - 1/x^7 + 1/x^6 + 1/x^3 Kauffman polynomial | x^13 y^5 - 4 x^13 y^3 + 3 x^13 y + x^12 y^6 - 4 x^12 y^4 + 3 x^12 y^2 + x^11 y^5 - 3 x^11 y^3 + x^11 y + x^10 y^4 - 3 x^10 y^2 + x^10 - x^8 y^4 + 3 x^8 y^2 - x^8 - x^7 y^3 + 2 x^7 y + x^6 y^6 - 6 x^6 y^4 + 9 x^6 y^2 - 3 x^6

    Properties

    chiral | hyperbolic | invertible | nonalternating | nonsatellite | nontorus | prime

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