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Discrete Mathematics and Combinatorics research

Discrete Mathematics and Combinatorics is a subfield of Mathematics. Science Explorer counts 62k research works in it since 1950. 10.1% 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%
6.2k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Topics
4
Growth, 2018-21 → 2022-25
+18%
the tick is no change
Largest producer
China
26% of the 10 largest, 2022-now
Discrete Mathematics and Combinatorics

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

By the world's output in 2021-25, its most used keywords are Finite Groups, Graphs, Combinatorics, Permutations, Graph Limits, Szemerédi's Theorem.

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

Size is the world's fractional works in 2021-25 in the topics tagged with each word; colour compares the word's share of this field with 2011-15. Each links to the topic it comes from most.

All 8 words, with their numbers
  1. Finite Groups3,679◆ 0.98×1 topic
  2. Graphs3,679◆ 0.98×1 topic
  3. Combinatorics3,312◆ 1.00×1 topic
  4. Permutations3,312◆ 1.00×1 topic
  5. Graph Limits2,546◆ 1.08×1 topic
  6. Szemerédi's Theorem2,546◆ 1.08×1 topic
  7. Fuzzy Fractal Dimensions1,030◆ 0.88×1 topic
  8. Granular Data1,030◆ 0.88×1 topic

Which countries lead Discrete Mathematics and Combinatorics research?

On research quality in 2022-now, the United States, China and the United Kingdom rank highest in Discrete Mathematics and Combinatorics. By volume, China and the United States publish the most (1.8k and 1.6k works in 2022-now).

By research quality, 2022-now

  1. 1 United States #1 all time 1.03× citation excellence · 1.51× journals · 100% breadth 11.0% top 10% · 1.4k works
  2. 2 China #4 all time 1.17× citation excellence · 0.89× journals · 100% breadth 11.9% top 10% · 1.5k works
  3. 3 United Kingdom #2 all time 1.25× citation excellence · 1.47× journals · 100% breadth 12.0% top 10% · 387 works
  4. 4 Germany #3 all time 1.12× citation excellence · 1.53× journals · 100% breadth 11.8% top 10% · 391 works
  5. 5 France #5 all time 0.89× citation excellence · 1.24× journals · 100% breadth 9.4% top 10% · 363 works
  6. 6 Canada #8 all time 0.97× citation excellence · 1.14× journals · 100% breadth 11.8% top 10% · 252 works
  7. 7 Italy #12 all time 1.34× citation excellence · 0.73× journals · 100% breadth 12.5% top 10% · 253 works
  8. 8 Japan #15 all time 0.69× citation excellence · 0.97× journals · 100% breadth 6.0% top 10% · 290 works
  9. 9 Russia #9 all time 0.92× citation excellence · 0.49× journals · 100% breadth 6.2% top 10% · 462 works
  10. 10 India #18 all time 0.89× citation excellence · 0.38× journals · 100% breadth 8.7% top 10% · 503 works

The track on each row is that row's top-10% rate. The ranking itself is the quality score, which compares the rate with what each place's own topics predict, adds its share of papers in the Nature Index journals, and counts output and breadth too.

Of 10 countries ranked in Discrete Mathematics and Combinatorics. Ranked on the quality score for 2022-now; the bracket is the all-time rank.

All countries ranked in Discrete Mathematics and Combinatorics

By volume, 2022-now

  1. 1 China 1.8k works
  2. 2 United States 1.6k works
  3. 3 India 610 works
  4. 4 Russia 505 works
  5. 5 United Kingdom 443 works
  6. 6 Germany 441 works
  7. 7 France 408 works
  8. 8 Japan 331 works
  9. 9 Italy 289 works
  10. 10 Canada 284 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: 26.1%United States: 24.5%India: 9.1%Russia: 7.5%6 others listed: 32.7%26%largest
China1,751 · 26.1%United States1,645 · 24.5%India610 · 9.1%Russia505 · 7.5%6 others listed2,195 · 32.7%

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-now, followed by Hungarian Academy of Sciences and Russian Academy of Sciences.

By research quality, 2022-now

  1. 1 Centre National de la Recherche Scientifique France · Paris · #5 all time 9.5% top 10% · 178 works
  2. 2 Hungarian Academy of Sciences Hungary · Budapest · #64 all time 10.0% top 10% · 61 works
  3. 3 Russian Academy of Sciences Russia · Moscow · #58 all time 6.6% top 10% · 129 works

The track on each row is that row's top-10% rate. The ranking itself is the quality score, which compares the rate with what each place's own topics predict, adds its share of papers in the Nature Index journals, and counts output and breadth too.

Of 3 institutions above the floor of 40 fractional works in Discrete Mathematics and Combinatorics.

Top 100 Discrete Mathematics and Combinatorics institutions

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 196 works
  2. 2 Russian Academy of SciencesRussia 140 works
  3. 3 Hungarian Academy of SciencesHungary 66 works
  4. 4 University of OxfordUnited Kingdom 53 works
  5. 5 ETH ZurichSwitzerland 50 works
  6. 6 Massachusetts Institute of TechnologyUnited States 45 works
  7. 7 Nankai UniversityChina 43 works
  8. 8 University of WaterlooCanada 38 works
  9. 9 University of WarwickUnited Kingdom 36 works
  10. 10 National Research University Higher School of EconomicsRussia 36 works

Who are the leading researchers in Discrete Mathematics and Combinatorics?

Counting only their work in Discrete Mathematics and Combinatorics, Terence Tao, Noga Alon and Benny Sudakov have the most papers in the world top 10% for their subfield and year beyond the 10% expected.

  1. 1 Terence Tao United States · #6,318 worldwide overall 32.9 of 47 papers here in the top 10%
  2. 2 Noga Alon Israel · #110,880 worldwide overall 39.7 of 133 papers here in the top 10%
  3. 3 Benny Sudakov Switzerland · #300,318 worldwide overall 31.1 of 122 papers here in the top 10%
  4. 4 George E. Andrews United States · #101,699 worldwide overall 27.2 of 87 papers here in the top 10%
  5. 5 Dae San Kim South Korea · #314,795 worldwide overall 31.8 of 93 papers here in the top 10%
  6. 6 Paul D. Seymour United States · #56,030 worldwide overall 21.7 of 61 papers here in the top 10%
  7. 7 Richard P. Stanley United States · #65,046 worldwide overall 19.4 of 45 papers here in the top 10%
  8. 8 Taekyun Kim South Korea · #605,474 worldwide overall 31.7 of 95 papers here in the top 10%
  9. 9 Jean Bourgain United States · #9,175 worldwide overall 15.3 of 31 papers here in the top 10%
  10. 10 Michael Krivelevich Israel · #499,105 worldwide overall 20.2 of 71 papers here in the top 10%

Ranked on their work in Discrete Mathematics and Combinatorics alone: how many more of their papers here reached the world top 10% for their subfield and year than the 10% expected, among 88,785 ranked researchers with a paper here. Each paper counts once, so many strong papers outrank one famous one, and a long record of ordinary papers does not climb. Identities come from OpenAlex author disambiguation, which occasionally merges or splits people.

Top 100 Discrete Mathematics and Combinatorics researchers

What are the most cited papers in Discrete Mathematics and Combinatorics?

The most cited paper in Discrete Mathematics and Combinatorics is "Spectral Graph Theory" (Fan Chung, 1996), with 5,771 citations. Next come "Communication and concurrency" (3,977) and "Partial differential equations of parabolic type" (3,305).

Most cited papers
#PaperReleasedCitations
1 Spectral Graph Theory Fan Chung · Regional conference series in mathematics Conference paper 3 Dec 1996 5,771
2 Communication and concurrency Wojciech Penczek · Science of Computer Programming Open access May 1990 3,977
3 Partial differential equations of parabolic type John S. Maybee · Journal of the Franklin Institute Jun 1965 3,305
4 A critical point for random graphs with a given degree sequence Michael S. O. Molloy, Bruce A. Reed · Random Structures and Algorithms Mar 1995 2,427
5 The Gaia Methodology for Agent-Oriented Analysis and Design Michael Wooldridge, Nicholas R. Jennings, David Kinny · Autonomous Agents and Multi-Agent Systems Open access Sep 2000 1,893
All 100 most cited papers, with filters and sorting

Where is Discrete Mathematics and Combinatorics research done?

The largest centres of Discrete Mathematics and Combinatorics research in 2022-now 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, Koper and Dolgoprudnyy.

Largest cities, 2022-now

  1. 1 MoscowRussia 231 works
  2. 2 BeijingChina 201 works
  3. 3 ParisFrance 138 works
  4. 4 ShanghaiChina 137 works
  5. 5 TokyoJapan 115 works
  6. 6 BudapestHungary 111 works
  7. 7 NanjingChina 94 works
  8. 8 TianjinChina 89 works
  9. 9 SeoulSouth Korea 78 works
  10. 10 LondonUnited Kingdom 71 works

Where it is the local speciality

  1. HomyelBY · 31.4 works62×
  2. KoperSI · 26.7 works46×
  3. DolgoprudnyyRU · 20.6 works18×
← 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, ETH Zurich, Massachusetts Institute of Technology and Stanford University score highest, combining standing in the field's ranking, citation excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%mean 15.01%fractional works in this field (log) →share of work in the world top 10% →Princeton UniversityStanford UniversityMassachusetts Instit…ETH Zurich
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Standingthis field's institution ranking, three quarters all time and a quarter 2022-now
50%
Citation excellenceshare of its work in the world top 10%, 2022-now and all time averaged
20%
Specialisationhow much of its work is in this field, counted up to 10× the world share
5%
Sizeits output in this field, on a log scale
15%
Growthoutput growth, counted from -20% to +20%
5%
Internationalshare of its work with a co-author abroad
5%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreRank in field (all time)Top 10%SpecialisationWorksGrowth
1ETH ZurichSwitzerland 84.3- (#1)10.2%8.5×50 +86.5%
2Massachusetts Institute of TechnologyUnited States 72.8- (#2)17.5%7.6×45 -14.0%
3Stanford UniversityUnited States 67.5- (#3)20.4%2.4×30 +36.8%
4Princeton UniversityUnited States 66.9- (#4)21.2%8.6×32 +73.1%
5University of California, Los AngelesUnited States 55.0- (#7)20.0%2.1×20 +54.4%
6University of OxfordUnited Kingdom 53.0- (#13)10.9%4.5×53 +48.3%
7University of CambridgeUnited Kingdom 52.8- (#10)14.0%3.3×33 +12.0%
8California Institute of TechnologyUnited States 51.3- (#6)7.8%5.6×17 +35.6%
9University of California San DiegoUnited States 49.5- (#9)12.2%3.0×24 +47.9%
10University of California, BerkeleyUnited States 47.8- (#8)15.9%2.5×20 -12.1%

Universities only. The score blends standing (50%), citation excellence (20%), size (15%), specialisation (5%), growth (5%), international reach (5%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise. Standing is the score in this field's institution ranking, three quarters over all time and a quarter 2022-now; excellence averages the two windows too. Four years alone undercount fields such as AI, where many conference and arXiv papers from 2022 on carry no affiliation in the data.

Every institution in Discrete Mathematics and Combinatorics, country by country

Is Discrete Mathematics and Combinatorics research growing?

Output in 2022-2025 was 18% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Limits and Structures in Graph Theory, Advanced Combinatorial Mathematics and Finite Group Theory Research.

still counting19801990200020102020
grewheldshrank

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

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Discrete Mathematics and Combinatorics as a percentage of every work published that year, 0.038% in 2024.

still counting0.050%0.10%0.15%Discrete Mathematics and Combinatorics0.037% in 202519801990200020102020

Fractional works of Discrete Mathematics and Combinatorics over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Discrete Mathematics and Combinatorics10.1% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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+26%
  2. Advanced Combinatorial Mathematics+16%
  3. Finite Group Theory Research+15%
  4. Modeling, Simulation, and Optimization+14%
← shrinkingno changegrowing →

Growth in output from 2018-21 to 2022-25. 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.

Share who leads Discrete Mathematics and Combinatorics

Who leads Discrete Mathematics and Combinatorics, on Science Explorer

A card with the countries and institutions that lead Discrete Mathematics and Combinatorics, for a post or a slide.

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1200 × 630 PNG, sized for social posts, drawn from the latest snapshot.

The leading institutions' badges3Each links to that institution's page and updates with every snapshot

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