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Subfield · Mathematics

Discrete Mathematics and Combinatorics research

Discrete Mathematics and Combinatorics is a subfield of Mathematics. Science Explorer counts 62k research works in it since 1950. 13.9% of them reached the world's top 10% most cited for their field and year.

In short: study of discrete mathematical structures.

Research works
62k
fractional, since 1950
In the world top 10%
8.6k
per year above
Top-10% rate
13.9%
share of its works in the world top 10%
Topics
4
Growth, 2013–17 → 2018–22
-3%
the tick is no change

What is Discrete Mathematics and Combinatorics research about, and what is growing?

By the world's output in 2019–23, its most used keywords are Finite Groups, Graphs, Combinatorics, Permutations, Graph Limits, Szemerédi's Theorem. Losing share: Fuzzy Fractal Dimensions, Granular Data.

▲ gaining share of this field◆ holding its share▼ losing share

Size is the world's fractional works in 2019–23 in the topics tagged with each word; colour compares the word's share of this field with 2009–13. Each links to the topic it comes from most.

All 8 words, with their numbers
  1. Finite Groups3,500◆ 0.98×1 topic
  2. Graphs3,500◆ 0.98×1 topic
  3. Combinatorics3,201◆ 1.05×1 topic
  4. Permutations3,201◆ 1.05×1 topic
  5. Graph Limits2,406◆ 1.10×1 topic
  6. Szemerédi's Theorem2,406◆ 1.10×1 topic
  7. Fuzzy Fractal Dimensions886▼ 0.76×1 topic
  8. Granular Data886▼ 0.76×1 topic

Which countries lead Discrete Mathematics and Combinatorics research?

On research quality in 2022–2025, China, the United States and the United Kingdom rank highest in Discrete Mathematics and Combinatorics. By volume, China and the United States publish the most (1.4k and 1.4k works in 2022–2025).

By research quality, 2022–2025

  1. 1 China · #2 all time 13.1% top 10% · 1.4k works
  2. 2 United States · #1 all time 12.4% top 10% · 1.4k works
  3. 3 United Kingdom · #3 all time 13.9% top 10% · 387 works
  4. 4 Germany · #5 all time 12.9% top 10% · 391 works
  5. 5 Russia · #6 all time 9.1% top 10% · 462 works
  6. 6 France · #4 all time 10.8% top 10% · 363 works
  7. 7 India · #13 all time 8.9% top 10% · 503 works
  8. 8 Italy · #11 all time 13.5% top 10% · 253 works
  9. 9 Canada · #8 all time 11.0% top 10% · 252 works
  10. 10 Japan · #7 all time 8.8% top 10% · 290 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 10 countries ranked in Discrete Mathematics and Combinatorics. Composite of field-normalised excellence (50%), output (30%) and citations (20%); the bracket is the all-time rank.

All countries ranked in Discrete Mathematics and Combinatorics

By volume, 2022–2025

  1. 1 China 1.4k works
  2. 2 United States 1.4k works
  3. 3 India 503 works
  4. 4 Russia 462 works
  5. 5 Germany 391 works
  6. 6 United Kingdom 387 works
  7. 7 France 363 works
  8. 8 Japan 290 works
  9. 9 Italy 253 works
  10. 10 Canada 252 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 25.1%United States: 24.5%India: 8.8%Russia: 8.0%6 others listed: 33.6%25%largest
China1,443 · 25.1%United States1,409 · 24.5%India503 · 8.8%Russia462 · 8.0%6 others listed1,936 · 33.6%

Shares of the rows listed above, not of the whole node.

Which institutions lead Discrete Mathematics and Combinatorics research?

Centre National de la Recherche Scientifique (France) ranks first in Discrete Mathematics and Combinatorics on research quality in 2022–2025, followed by .

By research quality, 2022–2025

  1. 1 Centre National de la Recherche Scientifique France · Paris · #7 all time 13.3% top 10% · 62 works

The track on each row is that row’s top-10% rate. The ranking itself is the composite score, which the rate is only one part of.

Of 1 institutions above the floor of 40 fractional works in Discrete Mathematics and Combinatorics.

Top 100 Discrete Mathematics and Combinatorics institutions

By volume, 2022–2025

  1. 1 Centre National de la Recherche Scientifique France 62 works
  2. 2 Alfréd Rényi Institute of Mathematics Hungary 59 works
  3. 3 University of Oxford United Kingdom 49 works
  4. 4 ETH Zurich Switzerland 45 works
  5. 5 Sobolev Institute of Mathematics Russia 37 works
  6. 6 Nankai University China 36 works
  7. 7 Massachusetts Institute of Technology United States 36 works
  8. 8 University of Waterloo Canada 33 works
  9. 9 National Research University Higher School of Economics Russia 32 works
  10. 10 University of Warwick United Kingdom 32 works

Who are the leading researchers in Discrete Mathematics and Combinatorics?

Among the most productive authors in Discrete Mathematics and Combinatorics, Stephan Ramon Garcia, Steven J. Miller and Donald E. Knuth rank highest on the composite score.

  1. 1 Stephan Ramon Garcia United States · #107 worldwide 4k citations · 136 works
  2. 2 Steven J. Miller United States · #283 worldwide 3.8k citations · 110 works
  3. 3 Donald E. Knuth United States · #357 worldwide 4k citations · 107 works
  4. 4 N. J. A. Sloane United States · #887 worldwide 2.8k citations · 116 works
  5. 5 H. S. M. Coxeter Canada · #1,398 worldwide 1.3k citations · 115 works
  6. 6 Richard M. Karp United States · #1,888 worldwide 2.6k citations · 79 works
  7. 7 Jeffrey C. Lagarias United States · #2,191 worldwide 1.9k citations · 76 works
  8. 8 Rudolf Ahlswede Germany · #2,461 worldwide 2.3k citations · 113 works
  9. 9 Terence Tao United States · #2,469 worldwide 3.1k citations · 215 works
  10. 10 Gilbert Strang United States · #2,821 worldwide 1k citations · 99 works

Re-ranked on the composite score from the 3,817 highest-output authors in Discrete Mathematics and Combinatorics. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Discrete Mathematics and Combinatorics researchers

Where is Discrete Mathematics and Combinatorics research done?

The largest centres of Discrete Mathematics and Combinatorics research in 2022–2025 are Moscow (Russia), Beijing (China), Paris (France) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Homyel and Koper.

Largest cities, 2022–2025

  1. 1 Moscow Russia 210 works
  2. 2 Beijing China 168 works
  3. 3 Paris France 124 works
  4. 4 Shanghai China 111 works
  5. 5 Budapest Hungary 102 works
  6. 6 Tokyo Japan 102 works
  7. 7 Nanjing China 78 works
  8. 8 Tianjin China 75 works
  9. 9 Seoul South Korea 69 works
  10. 10 London United Kingdom 63 works

Where it is the local speciality

  1. HomyelBY · 30.3 works68×
  2. KoperSI · 24.6 works50×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Discrete Mathematics and Combinatorics than the world average.

See Discrete Mathematics and Combinatorics on the map

Discrete Mathematics and Combinatorics research by country

The best places for Discrete Mathematics and Combinatorics research inside each country, with that country's researchers and world standing.

Where is the best place to study Discrete Mathematics and Combinatorics?

Among universities, judged by research, Kwangwoon University, Moscow Institute of Physics and Technology and Sogang University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%50%100%mean 29.37%fractional works in this node (log) →share in the world top 10% →Kwangwoon University: 10, 72.7%Moscow Institute of Physics and Technology: 18, 20.3%Sogang University: 10, 65.2%National Research University Higher School of Economics: 32, 13.3%ETH Zurich: 45, 16.0%Prince Mohammad bin Fahd University: 10, 27.5%University of Warwick: 32, 21.7%Belarusian State University: 9, 9.6%Indian Institute of Science Education and Research Mohali: 10, 13.8%Aligarh Muslim University: 14, 33.6%Kwangwoon UniversitySogang UniversityMoscow Institute of …National Research Un…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1Kwangwoon University South Korea 60.872.7%17.4×10 -27.5%
2Moscow Institute of Physics and Technology Russia 59.320.3%17.1×18 +260.2%
3Sogang University South Korea 59.065.2%15.7×10 -14.9%
4National Research University Higher School of Economics Russia 58.113.3%9.6×32 +165.5%
5ETH Zurich Switzerland 56.816.0%8.2×45 +42.1%
6Prince Mohammad bin Fahd University Saudi Arabia 53.827.5%19.2×10 —
7University of Warwick United Kingdom 52.221.7%8.7×32 -1.2%
8Belarusian State University Belarus 49.69.6%11.6×9 +254.1%
9Indian Institute of Science Education and Research Mohali India 49.313.8%19.9×10 +258.1%
10Aligarh Muslim University India 48.633.6%6.2×14 +145.6%

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Discrete Mathematics and Combinatorics research growing?

Output in 2018–2022 was 3% lower than in 2013–2017, peaking in 2023. The fastest-growing topics are Limits and Structures in Graph Theory, Advanced Combinatorial Mathematics and Finite Group Theory Research.

19801990200020102020
grewheldshrank

The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

  1. Limits and Structures in Graph Theory+29%
  2. Advanced Combinatorial Mathematics+26%
  3. Finite Group Theory Research+16%
  4. Modeling, Simulation, and Optimization+12%
← shrinkingno changegrowing →

Growth in output from 2005–09 to 2015–19. Every topic is a page of its own.

What does Discrete Mathematics and Combinatorics include?

Finite Group Theory Rese…24kFinite Group Theory Research: 24k fractional worksAdvanced Combinatorial M…18kAdvanced Combinatorial Mathematics: 18k fractional worksLimits and Structures in…13kLimits and Structures in Graph Theory: 13k fractional worksModeling, Simulation, and Optimization: 6,230 fractional works

Area is fractional works in that topic. Every name below is a page of its own.