Search results
Results From The WOW.Com Content Network
The Bruck–Ryser–Chowla theorem is a result on the combinatorics of block designs that implies nonexistence of certain kinds of design. It states that if a (v, b, r, k, λ)-design exists with v = b (a symmetric block design), then: if v is even, then k − λ is a square;
A theorem of Ryser provides the converse. If X is a v -element set, and B is a v -element set of k -element subsets (the "blocks"), such that any two distinct blocks have exactly λ points in common, then ( X, B ) is a symmetric block design.
He is best known for his 1949 paper coauthored with H. J. Ryser, the results of which became known as the Bruck–Ryser theorem (now known in a generalized form as the Bruck-Ryser-Chowla theorem), concerning the possible orders of finite projective planes. In 1946, he was awarded a Guggenheim Fellowship.
The existence of finite projective planes of other orders is an open question. The only general restriction known on the order is the Bruck–Ryser–Chowla theorem that if the order N is congruent to 1 or 2 mod 4, it must be the sum of two squares. This rules out N = 6.
Since every difference set gives an SBIBD, the parameter set must satisfy the Bruck–Ryser–Chowla theorem, but not every SBIBD gives a difference set. An Hadamard matrix of order m is an m × m matrix H whose entries are ±1 such that HH ⊤ = mI m, where H ⊤ is the transpose of H and I m is the m × m identity matrix.
Baranyai's theorem; Bertrand's ballot theorem; Bondy's theorem; Bruck–Ryser–Chowla theorem; C. Corners theorem; D. Dilworth's theorem; E. Erdős–Fuchs theorem ...
Brown's representability theorem (homotopy theory) Bruck–Chowla–Ryser theorem (combinatorics) Brun's theorem (number theory) Brun–Titchmarsh theorem (number theory) Brunn–Minkowski theorem (Riemannian geometry) Büchi-Elgot-Trakhtenbrot theorem (mathematical logic) Buckingham π theorem (dimensional analysis)
Bruck–Ryser–Chowla theorem; C. Cayley–Bacharach theorem; D. De Bruijn–Erdős theorem (incidence geometry) Desargues's theorem; F. Five points determine a conic;