Knot Invariant Comparison

`knot inv comparison`

Supplement to Big data comparison of quantum invariants [arXiv; GitHub].

For the same picture ordered by hyperbolic volume, see Detection Volume. For invariant distribution histograms, see Distribution.

uniquerandomrandomZoomed

(Note: We have high confidence in the data up to 16 crossings. Beyond that point, confidence drops due to the large volume of data (eg. unforeseen errors in the data or calculation).)

Restrict to a class of knots

allalternatingnon-alternating

Toggle successive quotients plot and data table.

Successive quotients

Table

Interactive plot: zoom, pan and toggle your desired invariants!

n	A2	A	B1	BV	BVSp	A+BV	ASp+BVSp	HFK2	HFK2T1	H	HH	J	K	KT1	KO	KR3	V1	V2	All	J+KT1
3	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
4	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
5	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
6	100	100	100	85.7142	85.7142	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
7	100	100	100	92.8571	92.8571	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
8	100	100	100	82.8571	82.8571	100	100	100	100	100	100	100	100	100	100	100	100	100	100	100
9	100	94.0476	100	92.8571	92.8571	100	100	95.238	92.8571	100	100	100	100	100	100	100	100	100	100	100
10	98.7951	84.7389	100	92.3694	92.3694	100	100	87.9518	83.5341	98.7951	99.5983	96.3855	96.3855	96.3855	96.3855	98.7951	100	100	100	96.38
11	95.8801	68.789	98.1273	97.1285	97.1285	99.5006	99.5006	79.4007	67.166	95.8801	96.2546	90.1373	91.136	90.7615	91.136	95.8801	98.2521	100	100	91.13
12	92.1397	59.5566	96.6745	96.9432	96.9432	99.3281	99.3281	71.3805	57.8098	92.2069	-	83.003	84.313	83.8427	84.1115	92.5428	97.1447	100	100	84.17
13	85.7153	43.494	92.3563	97.9483	97.9483	98.4959	98.4959	59.3135	42.0825	85.7308	-	73.3127	77.5086	77.1693	74.5314	86.4558	92.9348	99.6297	99.6297	77.44
14	81.2052	33.6953	89.3888	97.6508	97.6491	98.1347	98.1347	50.5764	32.5458	81.2152	-	64.4993	69.0441	68.4718	66.2812	82.4148	90.0712	99.446	99.446	68.97
15	76.4007	24.5519	86.213	97.7495	97.7447	97.8424	97.8424	43.2704	23.8227	76.409	-	55.7478	60.6918	59.8585	58.4002	78.2402	86.7314	99.1728	99.1731	60.64
16	74.0062	18.6575	83.8345	97.5302	97.5168	97.6063	97.606	38.9603	18.1512	74.0263	-	49.4228	54.7144	53.6317	53.2704	-	84.1575	99.0275	99.0288	54.67
17	73.6585	14.3524	-	97.7295	97.6921	97.7744	97.7428	35.826	14.0421	73.7008	-	44.8416	51.9372	50.4744	50.5784	-	-	-	-	51.9
18	73.8467	11.196	-	-	97.6499	-	97.7848	34.9569	11.0553	73.9172	-	41.6179	50.83	49.0012	49.4825	-	-	-	-	50.8
19	-	-	-	-	-	-	-	-	-	75.2121	-	40.1709	-	-	-	-	-	-	-	-

Note. Specialised invariants give approximations of the real values. However, the exact values must not be trusted due to adhoc mutations caused by floating point arithmetic.