Document Type
Article
Publication Date
1-1-2022
Abstract
An integer matrix A is Δ -modular if the determinant of each rank(A) × rank(A) submatrix has absolute value at most Δ. The class of 1-modular, or unimodular, matrices is of fundamental significance in both integer programming theory and matroid theory. A 1957 result of Heller shows that the maximum number of nonzero, pairwise non-parallel columns of a rank-r unimodular matrix is (r+1/2). We prove that, for each sufficiently large integer r, the maximum number of nonzero, pairwise non-parallel columns of a rank-r 2-modular matrix is (r+2/2) - 2.
Publication Source (Journal or Book title)
SIAM Journal on Discrete Mathematics
First Page
1231
Last Page
1248
Recommended Citation
Oxley, J., & Walsh, Z. (2022). 2-MODULAR MATRICES. SIAM Journal on Discrete Mathematics, 36 (2), 1231-1248. https://doi.org/10.1137/21M1419131