3 papers
cs.DM2026
On the existence of heavy columns in binary matrices with distinct rows
Jamolidin K. Abdurakhmanov
We investigate the existence of heavy columns in binary matrices with distinct rows. A column of an m x n binary matrix is called heavy if the number of ones in it is at least m/2.…
cs.DM2025
Distribution of codewords on the faces of a hypercube and new combinatorial identities
Jamolidin K. Abdurakhmanov
We present a novel framework for studying combinatorial identities through the geometric lens of subset distributions in q-valued cubes. By analyzing how elements of arbitrary subs…
cs.DM2025
The Combinatorial Rank of Subsets: Metric Density in Finite Hamming Spaces
Jamolidin K. Abdurakhmanov
We introduce a novel concept of rank for subsets of finite metric spaces E^n_q (the set of all n-dimensional vectors over an alphabet of size q) equipped with the Hamming distance,…