Combinatorics & Order Theory — Open Conjectures

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Combinatorics

# Conjecture Eponym(s) Comments
1 Dittert conjecture Eric Dittert  
2 Frankl conjecture Péter Frankl  
3 Hadamard conjecture Jacques Hadamard  

Order Theory

# Conjecture Eponym(s) Comments
1 1/3–2/3 conjecture Kislitsyn; Fredman; Linial In-repo formalization: statement + linear-extension counting, tightness of 1/3, duality & twin reductions proved; conjecture open
2 Gold partition conjecture —  

Additive Combinatorics

# Conjecture Eponym(s) Comments
1 Rudin’s conjecture Walter Rudin  

Other

# Conjecture Field Eponym(s) Comments
1 Scholz conjecture Addition chains Arnold Scholz  
2 Singmaster’s conjecture Binomial coefficients David Singmaster In-repo formalization: computable multiplicity, faithful counter; N(a)≥2, an infinite N≥4 family, and N(3003)≥8 proved (so C≥8, the conjectured value); uniform bound open

References

  • van Lint, J. H. & Wilson, R. M. A Course in Combinatorics. 2nd ed., Cambridge University Press, 2001.
  • Stanley, R. P. Enumerative Combinatorics. Vol. 1 & 2, Cambridge University Press.

For references on the formalized Dittert, Frankl, Gold partition, Hadamard, and Sensitivity conjectures, see the centralized bibliography.