India to the World

Mathematics & Computer Science

Combinatorics: permutations & combinations

9th-12th c. CEMahavira; Bhaskara IIGanita Sara Sangraha (850 CE); LilavatiPan-Indian / unspecified

801 CE

Systematic formulae for permutations and combinations, including factorial-type counting.

Dated: 801 CE–1200
As scholars put it: 9th-12th c. CE
Originator: Mahavira; Bhaskara II
Source text: Ganita Sara Sangraha (850 CE); Lilavati
Region: Pan-Indian / unspecified
Discipline: Mathematics & Computer Science
Evidence: Documented
Confidence: High
Verification: Verified-web

Meanwhile in the West

Formalised later in European combinatorics.

Fair to say

Combinatorial counting also appears in other traditions.

Path to modern innovation

Core to probability, cryptography, computer science.

801 CECombinatorics: permutations & combinations

1356Systematic generation of permutations

Builds on

200 BCEFibonacci-type sequence (matrameru)

Transmission

Independent development.

Primary sources

4Lilavati Of Bhaskaracharya 1908 Khemraj Khemraj, Internet ArchiveUnreviewed
5Lilavati Ganitamu Bhaskaracarya, Internet Archive, 1936Unreviewed

References

1Ganita Sara Sangraha (850)
2Lilavati (1150)

Further reading

Related

Binary numeral representation Pascal's triangle (Meru-prastara)

Corrections and additional sources: edit IND-014 on GitHub.