Advanced Combinatorial Mathematics
Advanced Combinatorial Mathematics is a research topic within Discrete Mathematics and Combinatorics. Science Explorer counts 18k research works in it since 1950. 18.9% of them reached the world's top 10% most cited for their field and year.
This cluster of papers covers a wide range of topics in combinatorial mathematics, including permutations, polytopes, algebraic combinatorics, enumerative combinatorics, Hopf algebras, Schubert calculus, toric varieties, Catalan numbers, and Ehrhart polynomials.
- Combinatorics
- Permutations
- Polytopes
- Algebraic Combinatorics
- Enumerative Combinatorics
- Hopf Algebras
- Schubert Calculus
- Toric Varieties
- Catalan Numbers
- Ehrhart Polynomials
- Research works
- 18k fractional, since 1950
- In the world top 10%
- 3.4k per year above
- Top-10% rate
- 18.9% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- -1% the tick is no change
Which countries lead Advanced Combinatorial Mathematics research?
By volume, the United States and China publish the most (620 and 358 works in 2022–2025).
By volume, 2022–2025
- 1 United States 620 works
- 2 China 358 works
- 3 France 165 works
- 4 India 147 works
- 5 Japan 137 works
- 6 Germany 132 works
- 7 United Kingdom 108 works
- 8 Canada 92 works
- 9 Russia 92 works
- 10 South Korea 86 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.
Shares of the rows listed above, not of the whole node.
Which institutions lead Advanced Combinatorial Mathematics research?
By volume in 2022–2025, Centre National de la Recherche Scientifique publishes the most Advanced Combinatorial Mathematics research, followed by National Research University Higher School of Economics and Massachusetts Institute of Technology.
By volume, 2022–2025
- 1 Centre National de la Recherche Scientifique France 30 works
- 2 National Research University Higher School of Economics Russia 16 works
- 3 Massachusetts Institute of Technology United States 14 works
- 4 University of Waterloo Canada 14 works
- 5 University of Oxford United Kingdom 13 works
- 6 Suzhou University of Science and Technology China 13 works
- 7 University of California, Davis United States 12 works
- 8 KTH Royal Institute of Technology Sweden 12 works
- 9 University of Michigan United States 12 works
- 10 University of California, Berkeley United States 11 works
Who are the leading researchers in Advanced Combinatorial Mathematics?
The most-cited researchers publishing on Advanced Combinatorial Mathematics include Donald E. Knuth, Steven J. Miller and Terence Tao.
- 1 Donald E. Knuth 4k citations
- 2 Steven J. Miller 3.8k citations
- 3 Terence Tao 3.1k citations
- 4 N. J. A. Sloane 2.8k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Advanced Combinatorial Mathematics research done?
The largest centres of Advanced Combinatorial Mathematics research in 2022–2025 are Moscow (Russia), Paris (France), Seoul (South Korea) and Tokyo (Japan).
Where is the best place to study Advanced Combinatorial Mathematics?
Among universities, judged by research, Kwangwoon University, Sogang University and National Research University Higher School of Economics 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.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Kwangwoon University South Korea | 60.7 | 72.7% | 55.2× | 10 | -25.7% |
| 2 | Sogang University South Korea | 60.5 | 69.2% | 46.5× | 10 | -0.8% |
| 3 | National Research University Higher School of Economics Russia | 57.7 | 14.7% | 15.3× | 16 | +237.3% |
| 4 | Suzhou University of Science and Technology China | 55.0 | 39.1% | 23.4× | 13 | — |
| 5 | Prince Mohammad bin Fahd University Saudi Arabia | 54.4 | 31.0% | 54.2× | 9 | — |
| 6 | KTH Royal Institute of Technology Sweden | 51.1 | 28.0% | 12.4× | 12 | -10.1% |
| 7 | Massachusetts Institute of Technology United States | 46.3 | 21.4% | 9.1× | 14 | +3.0% |
| 8 | University of Cologne Germany | 45.7 | 28.9% | 11.4× | 9 | +8.7% |
| 9 | University of Waterloo Canada | 43.7 | 8.0% | 9.8× | 14 | +7.1% |
| 10 | University of Virginia United States | 41.2 | 38.4% | 7.3× | 10 | +41.2% |
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 Advanced Combinatorial Mathematics research growing?
Output in 2018–2022 was 1% lower than in 2013–2017, peaking in 2025. The fastest-growing topics are Advanced Combinatorial Mathematics.
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.