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TY - CHAP
TI - PERFECT DIFFERENCE SETS
AU - RYSER, HERBERT JOHN
AB - Let$D = \{ {d_1},{d_2},.,{d_k}\} $be a*k*-set of integers modulo*v*such that every${\rm A} \ne 0$(mod*v*) can be expressed in exactly λ ways in the form (1.1)${d_i} - {d_j} \equiv a(\bmod v)$, where${d_i}$and${d_j}$are in*D*. We suppose further that (1.2)$0 < \lambda < k < v - 1$. The inequality (1.2) serves only to exclude certain degenerate configurations. A set*D*fulfilling these requirements is called a*perfect difference set*or, for brevity, a*difference set.*It is easy to verify that (1.3)$\lambda = \frac{{k(k - 1)}} {{v - 1}}$. This assertion is also an immediate consequence of the following theorem. THEOREM 1.1.*The perfect difference set D is equivalent to*$a(v,k,\lambda )$*-configuration with incidence*
EP - 142
ET - 1
PB - Mathematical Association of America
PY - 1963
SN - 9780883850473
SP - 131
T2 - Combinatorial Mathematics
UR - http://www.jstor.org/stable/10.4169/j.ctt5hh8v6.13
VL - 14
Y2 - 2021/07/23/
ER -