Class information for:
Level 1: BRAID GROUP//GARSIDE GROUPS//ARTIN GROUPS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
15085 732 17.1 40%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
281 3       MATHEMATICS//JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS//ALGEBRAIC AND GEOMETRIC TOPOLOGY 42804
1679 2             INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION//MATHEMATICS//CONJUGACY PROBLEM 6788
15085 1                   BRAID GROUP//GARSIDE GROUPS//ARTIN GROUPS 732

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 BRAID GROUP authKW 1500000 14% 35% 103
2 GARSIDE GROUPS authKW 711811 3% 74% 23
3 ARTIN GROUPS authKW 693049 5% 46% 36
4 CONJUGACY PROBLEM authKW 416531 4% 37% 27
5 ULTRA SUMMIT SET authKW 333709 1% 100% 8
6 MATH NICOLAS O ME address 299225 5% 18% 40
7 LOGARITHMIC SIGNATURES authKW 296628 1% 89% 8
8 CONJUGACY SEARCH PROBLEM authKW 255494 1% 88% 7
9 BRAID authKW 250645 3% 24% 25
10 ARTIN TITS GROUPS authKW 250282 1% 100% 6

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 25033 79% 0% 577
2 Mathematics, Applied 1668 20% 0% 145
3 Computer Science, Theory & Methods 1248 12% 0% 87
4 Computer Science, Information Systems 134 4% 0% 30
5 Logic 126 1% 0% 7
6 Computer Science, Interdisciplinary Applications 23 2% 0% 16
7 Physics, Mathematical 16 2% 0% 15
8 COMPUTER APPLICATIONS & CYBERNETICS 14 0% 0% 1
9 Computer Science, Software Engineering 10 1% 0% 10
10 Computer Science, Hardware & Architecture 1 1% 0% 4

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MATH NICOLAS O ME 299225 5% 18% 40
2 UMR 6139 210364 4% 16% 32
3 SDAD ESA 6081 125141 0% 100% 3
4 UMR CNRS 6139 104279 1% 50% 5
5 SDAD 97322 1% 33% 7
6 ARBEITSGRP COMP ALGEBRA SYSTEMSICHERHEIT 83427 0% 100% 2
7 CIENCIA COMP INTEL LIGENCIA ARTIFICIAL 83427 0% 100% 2
8 UMR 5584 56913 3% 7% 21
9 CIENCIA COMPUTAC INTELLIGENCIA ARTIFICIAL 55617 0% 67% 2
10 ANALYSE TOPOL PROBABILITE 41714 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS 65706 7% 3% 52
2 INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION 18879 3% 2% 22
3 APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 17561 2% 3% 16
4 JOURNAL OF ALGEBRA 8615 7% 0% 52
5 ALGEBRAIC AND GEOMETRIC TOPOLOGY 7924 2% 1% 15
6 COMMUNICATIONS IN ALGEBRA 6190 5% 0% 38
7 JOURNAL OF PURE AND APPLIED ALGEBRA 5983 4% 0% 29
8 ADVANCES IN MATHEMATICS OF COMMUNICATIONS 4102 1% 2% 6
9 DESIGNS CODES AND CRYPTOGRAPHY 4066 2% 1% 13
10 JOURNAL OF CRYPTOLOGY 3409 1% 1% 6

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 BRAID GROUP 1500000 14% 35% 103 Search BRAID+GROUP Search BRAID+GROUP
2 GARSIDE GROUPS 711811 3% 74% 23 Search GARSIDE+GROUPS Search GARSIDE+GROUPS
3 ARTIN GROUPS 693049 5% 46% 36 Search ARTIN+GROUPS Search ARTIN+GROUPS
4 CONJUGACY PROBLEM 416531 4% 37% 27 Search CONJUGACY+PROBLEM Search CONJUGACY+PROBLEM
5 ULTRA SUMMIT SET 333709 1% 100% 8 Search ULTRA+SUMMIT+SET Search ULTRA+SUMMIT+SET
6 LOGARITHMIC SIGNATURES 296628 1% 89% 8 Search LOGARITHMIC+SIGNATURES Search LOGARITHMIC+SIGNATURES
7 CONJUGACY SEARCH PROBLEM 255494 1% 88% 7 Search CONJUGACY+SEARCH+PROBLEM Search CONJUGACY+SEARCH+PROBLEM
8 BRAID 250645 3% 24% 25 Search BRAID Search BRAID
9 ARTIN TITS GROUPS 250282 1% 100% 6 Search ARTIN+TITS+GROUPS Search ARTIN+TITS+GROUPS
10 MOR CRYPTOSYSTEM 250282 1% 100% 6 Search MOR+CRYPTOSYSTEM Search MOR+CRYPTOSYSTEM

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 ZHU, P , WEN, QY , (2011) AFFINE BRAID GROUPS: A BETTER PLATFORM THAN BRAID GROUPS FOR CRYPTOLOGY?.APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING. VOL. 22. ISSUE 5-6. P. 375-391 36 88% 0
2 BELLINGERI, P , GODELLE, E , GUASCHI, J , (2017) ABELIAN AND METABELIAN QUOTIENT GROUPS OF SURFACE BRAID GROUPS.GLASGOW MATHEMATICAL JOURNAL. VOL. 59. ISSUE 1. P. 119 -142 18 95% 0
3 GODELLE, E , PARIS, L , (2013) PREGARSIDE MONOIDS AND GROUPS, PARABOLICITY, AMALGAMATION, AND FC PROPERTY.INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION. VOL. 23. ISSUE 6. P. 1431-1467 20 91% 1
4 DEHORNOY, P , (2011) THE SUBWORD REVERSING METHOD.INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION. VOL. 21. ISSUE 1-2. P. 71 -118 21 88% 6
5 DEHORNOY, P , (2016) LAVER'S RESULTS AND LOW-DIMENSIONAL TOPOLOGY.ARCHIVE FOR MATHEMATICAL LOGIC. VOL. 55. ISSUE 1-2. P. 49 -83 28 60% 0
6 WANG, XF , LI, G , YANG, L , LIN, HL , (2016) GROUPS WITH TWO GENERATORS HAVING UNSOLVABLE WORD PROBLEM AND PRESENTATIONS OF MIHAILOVA SUBGROUPS OF BRAID GROUPS.COMMUNICATIONS IN ALGEBRA. VOL. 44. ISSUE 7. P. 3020 -3037 17 89% 0
7 TSABAN, B , (2015) POLYNOMIAL-TIME SOLUTIONS OF COMPUTATIONAL PROBLEMS IN NONCOMMUTATIVE-ALGEBRAIC CRYPTOGRAPHY.JOURNAL OF CRYPTOLOGY. VOL. 28. ISSUE 3. P. 601 -622 15 100% 1
8 LEE, EK , CORRAN, R , LEE, SJ , (2015) BRAID GROUPS OF IMPRIMITIVE COMPLEX REFLECTION GROUPS.JOURNAL OF ALGEBRA. VOL. 427. ISSUE . P. 387 -425 22 69% 0
9 WANG, BC , HU, YP , (2014) SIGNATURE SCHEME USING THE ROOT EXTRACTION PROBLEM ON QUATERNIONS.JOURNAL OF APPLIED MATHEMATICS. VOL. . ISSUE . P. - 21 72% 0
10 LEE, SJ , LEE, EK , (2011) PERIODIC ELEMENTS IN GARSIDE GROUPS.JOURNAL OF PURE AND APPLIED ALGEBRA. VOL. 215. ISSUE 10. P. 2295 -2314 20 77% 1

Classes with closest relation at Level 1


Rank Class id link
1 13819 VIRTUAL KNOT//QUANDLE//JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
2 12903 HYPERPLANE ARRANGEMENT//RESONANCE VARIETY//CHARACTERISTIC VARIETY
3 21003 THOMPSONS GROUP//FINITENESS PROPERTIES//SIGMA INVARIANTS
4 13914 RESTARTING AUTOMATON//FINITE DERIVATION TYPE//AUTOMATIC SEMIGROUP
5 2654 FREE GROUP//CONJUGACY SEPARABLE//RELATIVELY HYPERBOLIC GROUPS
6 19219 DIAGONAL HARMONICS//AD NILPOTENT IDEAL//CYCLIC SIEVING PHENOMENON
7 14464 MAPPING CLASS GROUP//JOHNSON HOMOMORPHISM//TORELLI GROUP
8 21926 CYCLICALLY PRESENTED GROUP//CYCLIC PRESENTATIONS//FIBONACCI GROUP
9 15272 KAC MOODY GROUPS//TWIN BUILDINGS//COXETER GROUP
10 5722 TEICHMULLER SPACE//MAPPING CLASS GROUP//KLEINIAN GROUPS

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