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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. 10.1% 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%
1.8k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+16%
the tick is no change
Largest producer
United States
32% of the 10 largest, 2022-now
Advanced Combinatorial Mathematics

Which countries lead Advanced Combinatorial Mathematics research?

By volume, the United States and China publish the most (728 and 450 works in 2022-now).

By volume, 2022-now

  1. 1 United States 728 works
  2. 2 China 450 works
  3. 3 France 189 works
  4. 4 India 186 works
  5. 5 Japan 160 works
  6. 6 Germany 154 works
  7. 7 United Kingdom 128 works
  8. 8 Russia 107 works
  9. 9 Canada 103 works
  10. 10 South Korea 98 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.

United States: 31.6%China: 19.5%France: 8.2%India: 8.1%6 others listed: 32.6%32%largest
United States728 · 31.6%China450 · 19.5%France189 · 8.2%India186 · 8.1%6 others listed751 · 32.6%

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

Which institutions lead Advanced Combinatorial Mathematics research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Combinatorial Mathematics research, followed by Russian Academy of Sciences and Massachusetts Institute of Technology.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 97 works
  2. 2 Russian Academy of SciencesRussia 29 works
  3. 3 Massachusetts Institute of TechnologyUnited States 19 works
  4. 4 National Research University Higher School of EconomicsRussia 18 works
  5. 5 Max Planck SocietyGermany 18 works
  6. 6 Indian Institute of Technology KharagpurIndia 17 works
  7. 7 University of WaterlooCanada 16 works
  8. 8 University of OxfordUnited Kingdom 16 works
  9. 9 University of MichiganUnited States 15 works
  10. 10 Suzhou University of Science and TechnologyChina 14 works

Who are the leading researchers in Advanced Combinatorial Mathematics?

The most-cited researchers publishing on Advanced Combinatorial Mathematics include Richard A. Gibbs, Edward H. Witten and David L. Donoho.

  1. 1 Richard A. Gibbs United States 292k citations
  2. 2 Edward H. Witten United States 174k citations
  3. 3 David L. Donoho United States 154k citations
  4. 4 Susan Holmes United States 124k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Advanced Combinatorial Mathematics?

The most cited paper in Advanced Combinatorial Mathematics is "Communication and concurrency" (Wojciech Penczek, 1990), with 3,977 citations. Next come "On the resemblance and containment of documents" (1,741) and "Representations of Coxeter groups and Hecke algebras" (1,739).

Most cited papers
#PaperReleasedCitations
1 Communication and concurrency Wojciech Penczek · Science of Computer Programming Open access May 1990 3,977
2 On the resemblance and containment of documents Arndt Bröder Conference paper 22 Nov 2002 1,741
3 Representations of Coxeter groups and Hecke algebras David Kazhdan, G. Lusztig · Inventiones mathematicae Jun 1979 1,739
4 State models and the jones polynomial Louis Hirsch Kauffman · Topology Open access 1987 1,478
5 On the distribution of the length of the longest increasing subsequence of random permutations Jinho Baik, Percy A. Deift, Kurt Johansson · Journal of the American Mathematical Society 24 Jun 1999 1,257
All 100 most cited papers, with filters and sorting

Where is Advanced Combinatorial Mathematics research done?

The largest centres of Advanced Combinatorial Mathematics research in 2022-now are Moscow (Russia), Paris (France), Seoul (South Korea) and Tokyo (Japan).

Largest cities, 2022-now

  1. 1 MoscowRussia 69 works
  2. 2 ParisFrance 65 works
  3. 3 SeoulSouth Korea 54 works
  4. 4 TokyoJapan 53 works
  5. 5 BeijingChina 52 works
  6. 6 ShanghaiChina 39 works
  7. 7 TianjinChina 30 works
  8. 8 CambridgeUnited States 28 works
  9. 9 NanjingChina 25 works
  10. 10 New YorkUnited States 24 works
See Advanced Combinatorial Mathematics on the map

Where is the best place to study Advanced Combinatorial Mathematics?

Among universities, judged by research, Kwangwoon University, Sogang University and KTH Royal Institute of Technology 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%20%40%mean 22.81%fractional works in this field (log) →share of work in the world top 10% →Kwangwoon UniversitySogang UniversityKTH Royal Institute …Suzhou University of…
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.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Kwangwoon UniversitySouth Korea 72.046.2%57.9×11 +18.2%
2Sogang UniversitySouth Korea 71.045.9%48.9×11 +24.2%
3KTH Royal Institute of TechnologySweden 65.830.1%12.2×12 +83.7%
4Suzhou University of Science and TechnologyChina 64.925.4%23.9×14 +591.2%
5Massachusetts Institute of TechnologyUnited States 60.315.8%10.0×19 -36.8%
6National Research University Higher School of EconomicsRussia 56.910.2%16.4×18 +47.2%
7University of WaterlooCanada 56.911.7%10.8×16 +57.9%
8University of OxfordUnited Kingdom 55.811.2%4.1×16 +71.9%
9Prince Mohammad bin Fahd UniversitySaudi Arabia 55.820.4%55.1×9 +273.6%
10Indian Institute of Technology KharagpurIndia 53.911.2%12.3×17 +816.7%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Advanced Combinatorial Mathematics, country by country

Is Advanced Combinatorial Mathematics research growing?

Output in 2022-2025 was 16% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Advanced Combinatorial Mathematics.

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 Advanced Combinatorial Mathematics as a percentage of every work published that year, 0.011% in 2024.

still counting0.010%0.020%0.030%Advanced Combinatorial Mathematics0.012% in 202519801990200020102020

Fractional works of Advanced Combinatorial Mathematics 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%Advanced Combinatorial Mathematics10.1% 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.

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