# 9 47

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 Simple square depiction Threefold symmetrical depiction Ornate threefold symmetrical depiction

### Knot presentations

 Planar diagram presentation X6271 X16,8,17,7 X8394 X2,15,3,16 X14,9,15,10 X10,6,11,5 X4,14,5,13 X11,1,12,18 X17,13,18,12 Gauss code 1, -4, 3, -7, 6, -1, 2, -3, 5, -6, -8, 9, 7, -5, 4, -2, -9, 8 Dowker-Thistlethwaite code 6 8 10 16 14 -18 4 2 -12 Conway Notation [8*-20]

Minimum Braid Representative A Morse Link Presentation An Arc Presentation

Length is 9, width is 4,

Braid index is 4

[{5, 9}, {8, 1}, {9, 3}, {2, 7}, {4, 8}, {3, 6}, {1, 5}, {7, 4}, {6, 2}]
 Knot 9_47. A graph, knot 9_47. A part of a link and a part of a graph.

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 3 Bridge index 3 Super bridge index ${\displaystyle \{4,6\}}$ Nakanishi index 2 Maximal Thurston-Bennequin number [-2][-7] Hyperbolic Volume 10.05 A-Polynomial See Data:9 47/A-polynomial

### Four dimensional invariants

 Smooth 4 genus ${\displaystyle 1}$ Topological 4 genus ${\displaystyle 1}$ Concordance genus ${\displaystyle 3}$ Rasmussen s-Invariant -2

### Polynomial invariants

 Alexander polynomial ${\displaystyle t^{3}-4t^{2}+6t-5+6t^{-1}-4t^{-2}+t^{-3}}$ Conway polynomial ${\displaystyle z^{6}+2z^{4}-z^{2}+1}$ 2nd Alexander ideal (db, data sources) ${\displaystyle \{3,t+1\}}$ Determinant and Signature { 27, 2 } Jones polynomial ${\displaystyle 2q^{5}-4q^{4}+4q^{3}-5q^{2}+5q-3+3q^{-1}-q^{-2}}$ HOMFLY-PT polynomial (db, data sources) ${\displaystyle z^{6}a^{-2}+4z^{4}a^{-2}-z^{4}a^{-4}-z^{4}+4z^{2}a^{-2}-3z^{2}a^{-4}-2z^{2}+a^{-2}-2a^{-4}+a^{-6}+1}$ Kauffman polynomial (db, data sources) ${\displaystyle 2z^{7}a^{-1}+2z^{7}a^{-3}+6z^{6}a^{-2}+3z^{6}a^{-4}+3z^{6}+az^{5}-4z^{5}a^{-1}-4z^{5}a^{-3}+z^{5}a^{-5}-16z^{4}a^{-2}-7z^{4}a^{-4}-9z^{4}-2az^{3}+z^{3}a^{-1}+6z^{3}a^{-3}+3z^{3}a^{-5}+11z^{2}a^{-2}+9z^{2}a^{-4}+3z^{2}a^{-6}+5z^{2}-2za^{-1}-5za^{-3}-3za^{-5}-a^{-2}-2a^{-4}-a^{-6}+1}$ The A2 invariant ${\displaystyle -q^{6}+q^{4}+q^{2}+2+2q^{-2}-q^{-4}+q^{-6}-2q^{-8}-q^{-12}-q^{-14}+q^{-16}+q^{-20}}$ The G2 invariant ${\displaystyle q^{32}-2q^{30}+4q^{28}-7q^{26}+4q^{24}-q^{22}-8q^{20}+16q^{18}-16q^{16}+16q^{14}-4q^{12}-11q^{10}+20q^{8}-18q^{6}+14q^{4}-2q^{2}-13+21q^{-2}-8q^{-4}+13q^{-8}-19q^{-10}+18q^{-12}-4q^{-14}-9q^{-16}+12q^{-18}-21q^{-20}+25q^{-22}-13q^{-24}+9q^{-28}-19q^{-30}+23q^{-32}-18q^{-34}+4q^{-36}+3q^{-38}-14q^{-40}+19q^{-42}-11q^{-44}-3q^{-46}+15q^{-48}-19q^{-50}+12q^{-52}+q^{-54}-17q^{-56}+20q^{-58}-17q^{-60}+11q^{-62}+2q^{-64}-11q^{-66}+14q^{-68}-12q^{-70}+8q^{-72}-5q^{-76}+2q^{-78}-2q^{-80}+2q^{-82}-q^{-84}+2q^{-86}+q^{-88}}$

### "Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, ${\displaystyle q\leftrightarrow q^{-1}}$): {}

### Vassiliev invariants

 V2 and V3: (-1, -2)
V2,1 through V6,9:
 V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9 ${\displaystyle -4}$ ${\displaystyle -16}$ ${\displaystyle 8}$ ${\displaystyle -{\frac {110}{3}}}$ ${\displaystyle -{\frac {34}{3}}}$ ${\displaystyle 64}$ ${\displaystyle {\frac {32}{3}}}$ ${\displaystyle {\frac {32}{3}}}$ ${\displaystyle -16}$ ${\displaystyle -{\frac {32}{3}}}$ ${\displaystyle 128}$ ${\displaystyle {\frac {440}{3}}}$ ${\displaystyle {\frac {136}{3}}}$ ${\displaystyle {\frac {10529}{30}}}$ ${\displaystyle -{\frac {418}{15}}}$ ${\displaystyle {\frac {10738}{45}}}$ ${\displaystyle -{\frac {833}{18}}}$ ${\displaystyle {\frac {1409}{30}}}$

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

### Khovanov Homology

The coefficients of the monomials ${\displaystyle t^{r}q^{j}}$ are shown, along with their alternating sums ${\displaystyle \chi }$ (fixed ${\displaystyle j}$, alternation over ${\displaystyle r}$). The squares with yellow highlighting are those on the "critical diagonals", where ${\displaystyle j-2r=s+1}$ or ${\displaystyle j-2r=s-1}$, where ${\displaystyle s=}$2 is the signature of 9 47. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.
 \ r \ j \
-3-2-101234χ
11       22
9      2 -2
7     22 0
5    32  -1
3   22   0
1  24    2
-1 11     0
-3 2      2
-51       -1
Integral Khovanov Homology
 ${\displaystyle \dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}}$ ${\displaystyle i=1}$ ${\displaystyle i=3}$ ${\displaystyle r=-3}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=-2}$ ${\displaystyle {\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=-1}$ ${\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}}$ ${\displaystyle {\mathbb {Z} }^{2}}$ ${\displaystyle r=0}$ ${\displaystyle {\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }^{2}}$ ${\displaystyle r=1}$ ${\displaystyle {\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{3}}$ ${\displaystyle {\mathbb {Z} }^{3}}$ ${\displaystyle r=2}$ ${\displaystyle {\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}}$ ${\displaystyle {\mathbb {Z} }^{2}}$ ${\displaystyle r=3}$ ${\displaystyle {\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}}$ ${\displaystyle {\mathbb {Z} }^{2}}$ ${\displaystyle r=4}$ ${\displaystyle {\mathbb {Z} }_{2}^{2}}$ ${\displaystyle {\mathbb {Z} }^{2}}$