Canonical braids up to 10 crossings, lexicographically minimal among cyclic rotations and mirror images, with each generator appearing at least twice.

Snapshot changed; rerun validation.

length braid yakdb_id positive homogeneous is_minimum_braid minimum_braid
10 [1, 1, 1, 4, 3, 4, 3, 2, 1, 2] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 1, 4, 3, 4, 3, 2, 2, 2] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 1, 4, 3, 4, 3, 2, 3, 2] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 1, 4, 4, 3, 2, 3, 2, 4] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 1, 4, 4, 3, 2, 4, 3, 2] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 1, 4, 4, 4, 3, 2, 3, 2] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 1, 1, 2, 1, 2, 1, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 1, 2, 1, 2, 2, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 1, 2, 2, 1, 2, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 1, 2, 2, 2, 1, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 2, 1, 1, 2, 2, 2] 10_139 true true false [1, 1, 1, 1, 2, 1, 1, 1, 2, 2]
10 [1, 1, 2, 1, 2, 1, 2, 2, 1, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 2, 1, 2, 2, 2, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 2, 1, 3, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 2, 1, 4, 3, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 2, 2, 1, 1, 2, 2] 10_139 true true false [1, 1, 1, 1, 2, 1, 1, 1, 2, 2]
10 [1, 1, 2, 1, 2, 2, 1, 2, 1, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 2, 2, 2, 1, 2, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 2, 2, 2, 2, 2, 2] -9_1 true true false [1, 1, 1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 2, 2, 3, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 2, 2, 4, 3, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 2, 3, 2, 4, 3, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 2, 3, 4, 3, 2, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 2, 4, 3, 2, 4, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 2, 4, 3, 4, 3, 2] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 3, 2, 1, 4, 3, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 3, 2, 2, 4, 3, 4] 8_19 true true false [1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 3, 2, 3, 4, 3, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 3, 2, 3, 4, 4, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 3, 2, 4, 3, 2, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 3, 2, 4, 3, 4, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 3, 2, 4, 3, 4, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 3, 2, 4, 4, 3, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 3, 2, 4, 4, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 3, 4, 3, 2, 1, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 3, 4, 3, 2, 2, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 3, 4, 3, 2, 3, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 3, 4, 3, 2, 4, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 4, 3, 2, 1, 4, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 4, 3, 2, 2, 4, 3] 8_19 true true false [1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 1, 4, 3, 2, 3, 4, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 4, 3, 2, 3, 4, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 4, 3, 2, 4, 3, 2] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 4, 3, 2, 4, 3, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 4, 3, 2, 4, 4, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 4, 3, 4, 3, 2, 2] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 4, 3, 4, 3, 2, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 4, 4, 3, 2, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 1, 4, 4, 3, 2, 4, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 1, 4, 4, 4, 3, 2, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 2, 1, 1, 2, 2, 1, 2] 10_139 true true false [1, 1, 1, 1, 2, 1, 1, 1, 2, 2]
10 [1, 1, 2, 2, 1, 2, 1, 2, 2, 2] 10_139 true true false [1, 1, 1, 1, 2, 1, 1, 1, 2, 2]
10 [1, 1, 2, 2, 1, 2, 2, 2, 1, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 2, 1, 2, 2, 2, 2, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 2, 1, 2, 3, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 2, 1, 2, 4, 3, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 2, 1, 3, 2, 4, 3, 4] 8_19 true true false [1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 2, 1, 3, 4, 3, 2, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 2, 1, 4, 3, 2, 4, 3] 8_19 true true false [1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 2, 1, 4, 3, 4, 3, 2] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 2, 2, 1, 2, 1, 2, 2] 10_139 true true false [1, 1, 1, 1, 2, 1, 1, 1, 2, 2]
10 [1, 1, 2, 2, 2, 1, 2, 2, 2, 2] 10_139 true true false [1, 1, 1, 1, 2, 1, 1, 1, 2, 2]
10 [1, 1, 2, 2, 2, 1, 3, 4, 3, 4] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 2, 2, 1, 4, 3, 4, 3] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 2, 2, 2, 1, 2, 1, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 2, 2, 2, 1, 2, 2, 2] 10_139 true true false [1, 1, 1, 1, 2, 1, 1, 1, 2, 2]
10 [1, 1, 2, 2, 2, 2, 2, 1, 2, 2] 10_124 true true false [1, 1, 1, 1, 1, 2, 1, 1, 1, 2]
10 [1, 1, 2, 2, 2, 2, 2, 2, 1, 2] -9_1 true true false [1, 1, 1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 2, 3, 2, 1, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 2, 3, 4, 3, 2, 1, 4] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 2, 4, 3, 2, 1, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 2, 1, 2, 4, 3, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 3, 2, 1, 3, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 2, 1, 3, 4, 4, 4] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 3, 2, 1, 4, 3, 2, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 3, 2, 1, 4, 3, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 2, 1, 4, 3, 4, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 2, 1, 4, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 2, 1, 4, 4, 4, 3] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 3, 2, 2, 1, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 2, 4, 3, 2, 1, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 4, 3, 2, 1, 2, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 4, 3, 2, 1, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 4, 3, 2, 1, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 3, 4, 3, 2, 2, 1, 4] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 4, 3, 2, 1, 2, 4, 3] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 4, 3, 2, 1, 3, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 4, 3, 2, 1, 3, 4, 4] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 4, 3, 2, 1, 4, 3, 2] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]
10 [1, 1, 2, 4, 3, 2, 1, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 4, 3, 2, 1, 4, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 4, 3, 2, 2, 1, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 4, 3, 4, 3, 2, 1, 2] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 4, 3, 4, 3, 2, 1, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 4, 4, 3, 2, 1, 3, 4] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 2, 4, 4, 3, 2, 1, 4, 3] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 2, 4, 4, 4, 3, 2, 1, 3] -3_1 # -3_1 # -3_1 true true false [1, 1, 1, 2, 2, 2, 3, 3, 3]
10 [1, 1, 3, 2, 1, 2, 1, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 3, 2, 1, 2, 2, 4, 3, 4] -3_1 # -5_1 true true false [1, 1, 1, 1, 1, 2, 2, 2]
10 [1, 1, 3, 2, 1, 2, 4, 3, 2, 4] -7_1 true true false [1, 1, 1, 1, 1, 1, 1]

100 rows shown · 175970 matching rows · Normalized braids

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Metadata and schema

Provenance
Unknown / not supplied
Authors
Unknown / not supplied
Citations
Unknown / not supplied
Bibtex
Unknown / not supplied
License
Unknown / not supplied
Methodology
Legacy schema requires audit. Source payloads are preserved; name-based joins are uncertified.
Completeness
Unknown / not supplied

Name-based joins are uncertified.

ColumnTypeDescription
lengthintLength of the braid
braidmathematica_short_codeBraid word used to compute $F_K$
yakdb_idstringYakDB ID
positiveboolIs the braid positive?
homogeneousboolIs the braid homogeneous?
is_minimum_braidboolIs the braid a minimum braid?
minimum_braidmathematica_short_codeShortest braid word for this knot

Schema version: 80a86895da2bbd7e6da60d9058976a8d842c24ee10273bb248c18cf30de8e616 · Data version: unversioned-synapse

REST API

JSON rows for the current filters: GET https://topology.fyi/api/v1/datasets/hard_braids/rows?raw=1

Schema: /api/v1/datasets/hard_braids/schema

curl "https://topology.fyi/api/v1/datasets/hard_braids/rows?raw=1"