Báo cáo toán học: "Balancing cyclic R-ary Gray codes" potx

... has the Hamiltonian cycles for the cyclic Gray codes in (1). Figure 1: cyclic 2-digit R-ary Gray codes for R = 2, 3, 4. The transition sequence of a cyclic Gray code records the successive digit ... When R is even, the cyclicness forces every transition count to be even and so (unlike the cyclic ternary code given above in (1)) for even R every well-balanced cyclic R-ary...

Ngày tải lên: 07/08/2014, 15:22

... R n , our construction yields a balanced cyclic n-digit R-ary Gray code. (b) If n divides R n , our construction yields a uniform cyclic n-digit R-ary Gray code when R ≡ 0 (mod 4). When R ≡ 2 ... constructing close-to-uniform cyclic n-digit R-ary Gray codes for R ≥ 3. Similar to the binary case, it is helpful to picture the vertices of the n-digit R-ary Gray graph as arr...

Ngày tải lên: 07/08/2014, 21:20

... together the old and new results on cyclic solutions to OP(r, r, s) for small values of r. Theorem 3.4 Except for the insoluble case OP(3, 3, 5), there is a cyclic solution to OP(r, r, s) for ... ≤ 8. Table 2 of [12] gives cyclic solutions for all s in the range 5 ≤ s ≤ N r ,whereN r is taken from Table 1. For r in the range 9 ≤ r ≤ 13, Table 2 of [12] gives cyclic solutions for 5 ≤ s...

Ngày tải lên: 07/08/2014, 13:21

... In this paper, we pr ove the cyclic sieving phenomenon, introduced by Reiner-Stanton- White, for faces of an even-dimensional cyclic polytope, under a group action that cyclically translates the ... of a cyclic group. Let X be a finite set, X(q) a polynomial in Z[q] with the property X(1) = |X|, a nd C a finite cyclic group acting on X. The triple (X, X(q), C) is said to exhibit the cy...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 06/08/2014, 04:21

Ngày tải lên: 07/08/2014, 06:20

Ngày tải lên: 07/08/2014, 06:20