Knot Invariant Comparison

`knot inv comparison`

Supplement to Big data comparison of quantum invariants [arXiv; GitHub]. For statistics of the polynomials, see Stats.

unique

Toggle successive quotients plot and data table.

Successive quotients

Table

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

n	A2	A	B1	BV	A+BV	HFK2	HFK2T1	H	J	K	KT1	KO
0	100	93.75	100	100	100	93.75	93.75	100	100	100	100	100
1	100	93.75	100	100	100	93.75	93.75	100	100	100	100	100
2	100	94.1176	100	100	100	94.1176	94.1176	100	100	100	100	100
3	100	95.6521	100	100	100	95.6521	95.6521	100	100	100	100	100
4	100	79.5454	100	100	100	97.7272	79.5454	100	100	100	100	100
5	100	82.6666	100	98.6666	100	93.3333	78.6666	100	97.3333	100	100	100
6	99.27	79.562	100	97.8102	100	89.781	75.9124	99.27	96.3503	100	99.27	100
7	99.526	79.6208	100	98.1042	100	89.5734	73.9336	99.526	94.7867	100	99.0521	99.526
8	99.4065	80.7121	100	98.5163	100	90.8011	71.5133	99.4065	93.175	99.7032	99.1097	98.5163
9	98.9778	76.4906	99.4889	97.4446	99.3185	89.7785	65.9284	98.9778	91.8228	98.8074	97.9557	97.2742
10	98.4771	73.604	99.3908	97.868	99.1878	90.0507	63.4517	98.4771	90.0507	97.5634	96.5482	95.6345
11	97.3669	67.1148	99.2717	97.9831	98.8795	88.0672	57.0308	97.3669	87.8431	96.6946	95.07	93.3893
12	96.3325	61.2393	99.1147	98.1662	98.8934	85.5516	51.8495	96.3958	84.1606	94.5305	92.1593	90.9263
13	94.3185	54.5132	98.3185	98.3185	98.8849	82.0884	45.7876	94.4778	79.4159	92.1946	89.3451	87.5929
14	92.6275	49.0859	97.7701	98.4029	98.8549	78.8469	40.8798	92.7581	75.5222	89.3431	85.9783	84.321
15	90.4954	43.6778	96.8318	98.5325	98.8624	75.5929	36.6532	90.5978	71.1392	85.9393	82.4697	80.6154
16	87.7744	38.6369	95.5469	98.3174	98.569	71.9419	32.5927	87.8822	66.7537	82.1157	78.3389	76.5126
17	85.319	33.8412	94.3521	98.2796	98.4667	68.0433	28.7489	85.4145	62.468	78.1723	74.0978	72.5856
18	82.5958	29.6647	92.9942	98.106	98.2536	64.1698	25.468	82.6696	58.4165	73.8767	69.805	68.5197
19	80.3108	25.9663	91.6229	97.9929	98.106	60.3564	22.5259	80.3771	55.207	70.0663	66.2205	65.1709
20	78.1569	22.9615	90.1241	97.8262	97.9175	56.7159	20.2325	78.2194	52.3228	66.3077	62.7668	61.8681
21	76.3257	20.6036	88.6368	97.6732	97.7486	53.3522	18.4365	76.3795	50.164	63.0762	59.8863	59.1319
22	74.8246	18.7091	87.1559	97.5143	97.5797	50.2042	16.9918	74.8698	48.4311	60.1422	57.3723	56.7123
23	73.6122	17.3298	85.8387	97.4059	97.4646	47.188	15.9683	73.6524	47.2078	57.654	55.2933	54.6972
24	72.7533	16.4705	84.6727	97.3125	97.3693	44.4953	15.3955	72.7871	46.5158	55.7072	53.732	53.1669
25	72.3771	16.0884	83.8933	97.2772	97.3324	42.2485	15.2294	72.4065	46.37	54.4073	52.7347	52.2133
26	72.3794	16.1153	83.4537	97.3	97.3542	40.506	15.4028	72.4052	46.6556	53.7474	52.292	51.8149
27	72.6445	16.4496	83.3128	97.3493	97.4052	39.37	15.8276	72.6682	47.2042	53.608	52.2977	51.8611
28	73.0197	16.9362	83.3628	97.4024	97.4607	38.8012	16.3658	73.0421	47.8289	53.7747	52.558	52.1525
29	73.3164	17.4401	83.4373	97.442	97.5041	38.5883	16.8996	73.3378	48.3496	53.9954	52.8402	52.4548
30	73.5707	17.8966	83.5507	97.4794	97.5449	38.6135	17.3738	73.5915	48.7395	54.2035	53.0856	52.7125
31	73.779	18.2698	83.6796	97.5108	97.5794	38.7357	17.7568	73.7993	49.0489	54.4097	53.3129	52.9468
32	73.9223	18.5009	83.7765	97.5259	97.5981	38.8553	17.9925	73.9425	49.2743	54.5872	53.5002	53.1374
33	73.9846	18.6126	83.82	97.5307	97.6046	38.9276	18.1058	74.0048	49.3839	54.6803	53.5966	53.2349
34	74.0027	18.6485	83.8324	97.5307	97.6059	38.9535	18.1421	74.0228	49.4164	54.7087	53.6259	53.2645
35	74.0059	18.6567	83.8344	97.5304	97.6062	38.9596	18.1504	74.026	49.4223	54.7139	53.6312	53.2699
36	74.0062	18.6575	83.8345	97.5302	97.6063	38.9602	18.1512	74.0263	49.4228	54.7144	53.6317	53.2703
37	74.0062	18.6575	83.8345	97.5302	97.6063	38.9603	18.1512	74.0263	49.4228	54.7144	53.6317	53.2704

The following table shows abbreviations used in some of the plots and their descriptions. For convenience, names may also be attained by hovering over the headings in the data table above.

Name	Abbreivation	Description
A2	A2	SL3 polynomial
Alexander	A	Alexander polynomial
B1	B1	SO3 Polynonmial; 2 coloured Jones polynomial
BV	BV	Bar-Natan and van der Veen's Theta (non Alexander part)
Alexander+BV	A+BV	Bar-Natan and van der Veen's Theta (full)
HFK2	HFK2	HFK homology (p=2)
HFK2T1	HFK2T1	HFK homology (p=2) specialising t=1
HOMFLYPT	H	HOMFLYPT polynomial
Jones	J	Jones polynomial
Khovanov	K	Khovanov homology
KhovanovT1	KT1	Khovanov homology specialising t=1
KhovanovOdd	KO	Odd Khovanov homology