Incidence Matrices of Subsets—A Rank Formula

DOI10.1137/0602037zbMath0499.05017OpenAlexW2026135987MaRDI QIDQ3964584

Nathan Linial, Bruce L. Rothschild

Publication date: 1981

Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0602037

zbMATH Keywords

extremal set theory(0,1)-matrices

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Permutations, words, matrices (05A05) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Combinatorial aspects of matroids and geometric lattices (05B35) Combinatorial codes (94B25)

Related Items

On the fast algebraic immunity of threshold functions, On the rank of higher inclusion matrices, Kernels of modular inclusion maps, Holographic algorithms: from art to science, Signature theory in holographic algorithms, Rank of inclusion matrices and modular representation theory, The \(k\)-orbit reconstruction and the orbit algebra, Resilience of ranks of higher inclusion matrices, Cohomological Aspects of Hypergraphs, Some properties of a higher-order coboundary operator, Intersection theorems and mod \(p\) rank of inclusion matrices, A diagonal form for the incidence matrices of \(t\)-subsets vs. \(k\)- subsets, Intersection patterns of convex sets, Moore-Penrose inverse of set inclusion matrices

Cites Work

• On theory and applications of BIB designs with repeated blocks
• On the Structure oft-Designs