The Knowlton-Graham partition problem
Donald E. Knuth
Abstract
A set partition technique that is useful for identifying wires in cables can be recast in the language of 0--1 matrices, thereby resolving an open problem stated by R.~L. Graham in Volume 1 of this journal. The proof involves a construction of 0--1 matrices having row and column sums without gaps.
Create a lesson
Related papers
Off-Diagonal Induced Ramsey Numbers
Bruno Andrades, Marcelo Campos, Rafael Filipe et al.
Largest Sperner families with bounded VC-dimension
Gennian Ge, Hanyu Wang, Zixiang Xu et al.
Proof of two conjectures on the log-concavity of partition ranks and cranks
Jianxi Mao, Wenle Shi, Bao-Xuan Zhu
The Exact Number of Pentagons in Book-Free Graphs
Wentao Hu
A family of symmetric counterexamples to the bent sum decomposition conjecture
Máté Róbert Kepes, Anita Kercsó-Molnár, Viczián András
Counting graphs admitting a strictly matched involution
Stephan Dominique Andres, Igor Režan