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Values Of Minors Of An Infinite Family Of D-Optimal Designs And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Values Of Minors Of An Infinite Family Of D-Optimal Designs And Their Application To The Growth Problem, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We obtain explicit formulae for the values of the 2v — j minors, j = 0, 1, 2 of D-optimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of either two SBIBD(2s2 + 2s + 1, s2, s2-s/2) or 2 — {2s2 + 2s + 1; s2, s2; s(s–1)} sds. This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our theoretical formulae imply growth greater than 2(2s2 + 2s + 1) but experimentation has not …
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Values Of Minors Of (1,-1) Incidence Matrices Of Sbibds And Their Application To The Growth Problem, C Koukouvinos, M Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We obtain explicit formulae for the values of the v j minors, j = 0, 1,2 of (1, -1) incidence matrices of SBIBD(v, k, λ). This allows us to obtain explicit information on the growth problem for families of matrices with moderate growth. An open problem remains to establish whether the (1, -1) CP incidence matrices of SBIBD(v, k, λ), can have growth greater than v for families other than Hadamard families.
An Infinite Family Of Hadamard Matrices With Fourth Last Pivot N/2, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
An Infinite Family Of Hadamard Matrices With Fourth Last Pivot N/2, C. Koukouvinos, M. Mitrouli, Jennifer Seberry
Professor Jennifer Seberry
We show that the equivalence class of Sylvester Hadamard matrices give an infinite family of Hadamard matrices in which the fourth last pivot is n/2 . Analytical examples of Hadamard matrices of order n having as fourth last pivot n/2 are given for n = 16 and 32. In each case this distinguished case with the fourth pivot n/2 arose in the equivalence class containing the Sylvester Hadamard matrix.