rank bound

2020-09-03 / Last updated : 2020-09-03 Ferdinand Ihringer Mathematics

Almost a Hadamard Matrix

Recently, Yu Hin Au, Nathan Lindzey, and Levent Tunçel published a preprint with various spectral bounds on the arXiv. They investigate generalizations of bounds due to Delsarte and Hoffman in the context of the Lovász-Schrijver SDP. Page 12 of that article I knew for a few more days because Nathan asked me if their bound […]

2019-07-27 / Last updated : 2019-07-27 Ferdinand Ihringer Mathematics

Huang’s Breakthrough, Cvetković’s Bound, Godsil’s Question, and Sinkovic’s Answer

Let us consider the $ {n}$-dimensional hypercube $ {\{ 0, 1 \}^n}$. The Hamming graph on $ {H_n}$ has the elements of $ {\{ 0, 1 \}^n}$ as vertices an two vertices are adjacent if their Hamming distance is one, so they differ in one coordinate. It is easy to see that the independence number […]