Class information for:
Level 1: 3X1 PROBLEM//COLLATZ PROBLEM//3X1 CONJECTURE

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
30095 174 13.2 32%


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
485 3       LINEAR ALGEBRA AND ITS APPLICATIONS//BENFORDS LAW//MATHEMATICS, APPLIED 23484
3563 2             BENFORDS LAW//CESTAC METHOD//3X1 PROBLEM 1323
30095 1                   3X1 PROBLEM//COLLATZ PROBLEM//3X1 CONJECTURE 174

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 3X1 PROBLEM authKW 1974269 9% 75% 15
2 COLLATZ PROBLEM authKW 1184561 5% 75% 9
3 3X1 CONJECTURE authKW 1052948 3% 100% 6
4 COLLATZ CONJECTURE authKW 1021036 5% 73% 8
5 BUSY BEAVER authKW 701965 2% 100% 4
6 SMALL UNIVERSAL TURING MACHINES authKW 701965 2% 100% 4
7 3N1 PROBLEM authKW 626752 3% 71% 5
8 3N1 CONJECTURE authKW 526474 2% 100% 3
9 INTEGRAL FUNCTIONAL EQUATIONS authKW 526474 2% 100% 3
10 SYRACUSE PROBLEM authKW 526474 2% 100% 3

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 2618 53% 0% 92
2 Mathematics, Applied 952 30% 0% 52
3 Computer Science, Theory & Methods 605 17% 0% 29
4 Logic 184 2% 0% 4
5 Computer Science, Software Engineering 56 5% 0% 8
6 Computer Science, Cybernetics 54 2% 0% 3
7 Physics, Mathematical 17 3% 0% 6
8 Statistics & Probability 9 2% 0% 4
9 Computer Science, Information Systems 7 2% 0% 4
10 Automation & Control Systems 7 2% 0% 3

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 C C MOL 175491 1% 100% 1
2 DEF AUSTRALIA HMAS STIRLING 175491 1% 100% 1
3 EUIPE LOG 175491 1% 100% 1
4 MAT EST 175491 1% 100% 1
5 UFREA 3097 175491 1% 100% 1
6 UNIV TECHNOL METZ INFORMAT 175491 1% 100% 1
7 GRP INFORMAT FONDAMENTALE METZ 175489 1% 50% 2
8 BOOLE INFORMAT 93588 2% 13% 4
9 INESC AVEIRO 87745 1% 50% 1
10 TASS GRP 87745 1% 50% 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 ACTA ARITHMETICA 15766 10% 1% 17
2 MATHEMATICS MAGAZINE 11138 1% 3% 2
3 FIBONACCI QUARTERLY 5520 3% 1% 6
4 ADVANCES IN APPLIED MATHEMATICS 4391 3% 0% 6
5 COMPUTATIONAL METHODS AND FUNCTION THEORY 4385 1% 3% 1
6 THEORETICAL COMPUTER SCIENCE 4180 9% 0% 16
7 AMERICAN MATHEMATICAL MONTHLY 4148 5% 0% 8
8 INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING 2958 1% 1% 2
9 MATHEMATICS OF COMPUTATION 2820 5% 0% 8
10 EXPERIMENTAL MATHEMATICS 2170 2% 0% 3

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 3X1 PROBLEM 1974269 9% 75% 15 Search 3X1+PROBLEM Search 3X1+PROBLEM
2 COLLATZ PROBLEM 1184561 5% 75% 9 Search COLLATZ+PROBLEM Search COLLATZ+PROBLEM
3 3X1 CONJECTURE 1052948 3% 100% 6 Search 3X1+CONJECTURE Search 3X1+CONJECTURE
4 COLLATZ CONJECTURE 1021036 5% 73% 8 Search COLLATZ+CONJECTURE Search COLLATZ+CONJECTURE
5 BUSY BEAVER 701965 2% 100% 4 Search BUSY+BEAVER Search BUSY+BEAVER
6 SMALL UNIVERSAL TURING MACHINES 701965 2% 100% 4 Search SMALL+UNIVERSAL+TURING+MACHINES Search SMALL+UNIVERSAL+TURING+MACHINES
7 3N1 PROBLEM 626752 3% 71% 5 Search 3N1+PROBLEM Search 3N1+PROBLEM
8 3N1 CONJECTURE 526474 2% 100% 3 Search 3N1+CONJECTURE Search 3N1+CONJECTURE
9 INTEGRAL FUNCTIONAL EQUATIONS 526474 2% 100% 3 Search INTEGRAL+FUNCTIONAL+EQUATIONS Search INTEGRAL+FUNCTIONAL+EQUATIONS
10 SYRACUSE PROBLEM 526474 2% 100% 3 Search SYRACUSE+PROBLEM Search SYRACUSE+PROBLEM

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 LAARHOVEN, T , DE WEGER, B , (2013) THE COLLATZ CONJECTURE AND DE BRUIJN GRAPHS.INDAGATIONES MATHEMATICAE-NEW SERIES. VOL. 24. ISSUE 4. P. 971 -983 11 92% 0
2 WOODS, D , NEARY, T , (2015) YURII ROGOZHIN'S CONTRIBUTIONS TO THE FIELD OF SMALL UNIVERSAL TURING MACHINES.FUNDAMENTA INFORMATICAE. VOL. 138. ISSUE 1-2. P. 251 -258 10 91% 0
3 FENG, DG , FAN, XB , DING, LP , WANG, ZY , (2012) ON THE NONEXISTENCE OF NONTRIVIAL SMALL CYCLES OF THE MU FUNCTION IN 3X+1 CONJECTURE.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY. VOL. 25. ISSUE 6. P. 1215 -1222 9 100% 0
4 WOODS, D , NEARY, T , (2009) THE COMPLEXITY OF SMALL UNIVERSAL TURING MACHINES: A SURVEY.THEORETICAL COMPUTER SCIENCE. VOL. 410. ISSUE 4-5. P. 443-450 14 67% 8
5 MONKS, K , MONKS, KG , MONKS, KM , MONKS, M , (2013) STRONGLY SUFFICIENT SETS AND THE DISTRIBUTION OF ARITHMETIC SEQUENCES IN THE 3X+1 GRAPH.DISCRETE MATHEMATICS. VOL. 313. ISSUE 4. P. 468-489 8 100% 1
6 WANG, XY , YU, XJ , (2008) DYNAMICS OF THE GENERALIZED 3X+1 FUNCTION DETERMINED BY ITS FRACTAL IMAGES.PROGRESS IN NATURAL SCIENCE-MATERIALS INTERNATIONAL. VOL. 18. ISSUE 2. P. 217 -223 9 100% 0
7 WANG, XY , YU, XJ , (2007) VISUALIZING GENERALIZED 3X+1 FUNCTION DYNAMICS BASED ON FRACTAL.APPLIED MATHEMATICS AND COMPUTATION. VOL. 188. ISSUE 1. P. 234-243 9 100% 0
8 NEARY, T , WOODS, D , (2009) FOUR SMALL UNIVERSAL TURING MACHINES.FUNDAMENTA INFORMATICAE. VOL. 91. ISSUE 1. P. 123-144 8 100% 10
9 WOODS, D , NEARY, T , (2009) SMALL SEMI-WEAKLY UNIVERSAL TURING MACHINES.FUNDAMENTA INFORMATICAE. VOL. 91. ISSUE 1. P. 179-195 9 90% 2
10 MICHEL, P , (2015) PROBLEMS IN NUMBER THEORY FROM BUSY BEAVER COMPETITION.LOGICAL METHODS IN COMPUTER SCIENCE. VOL. 11. ISSUE 4. P. - 7 100% 0

Classes with closest relation at Level 1


Rank Class id link
1 32449 DIVERGENT PERMUTATIONS//UNIVERSAL FUZZY MEASURE//ASYMPTOTIC FUZZY MEASURE
2 37371 ISOMORPHIC FACTORS//PL MATH FEI//ALMOST COMPLETE TRIPARTITE GRAPH
3 33449 POLYADIC GROUPS//WARINGS PROBLEM//N M SEMIGROUP
4 17404 HYPERCOMPUTATION//CHURCH TURING THESIS//ANALOG COMPUTATION
5 32030 NORMALIZED COMPRESSION DISTANCE//WORD REMOVAL//INFORMATION DISTANCE
6 11719 DNA COMPUTING//DNA COMPUTATION//SPLICING SYSTEMS
7 16946 MAHLER MEASURE//SALEM NUMBERS//EXPLICIT AUXILIARY FUNCTION
8 22671 BENFORDS LAW//FIRST DIGIT LAW//MANTISSA
9 25940 PICTURE LANGUAGES//TWO DIMENSIONAL LANGUAGES//2D LANGUAGES
10 12007 MEMBRANE COMPUTING//P SYSTEMS//GRP NAT COMP

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