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 forcesevery transition count to be even and so (unlike the cyclic ternary code given abovein (1)) for even R every well-balanced cyclic R-ary Gray code must be ... 2)2/2 ,the code produced is a cyclic 2-digit (R + 2)-ary Gray code with the required transitioncounts.Theorem 2. For any R ≥ 2 there exists a cyclic 2-digit R-ary Gray code which is well-balanced,...

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

... Rn, our construction yields a balanced cyclic n-digit R-ary Gray code.(b) If n divides Rn, our construction yields a uniform cyclic n-digit R-ary Gray codewhen 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 topicture the vertices of the n-digit R-ary Gray graph as arranged in a rectangular ... is called cyclic. For example,20, 21, 22, 12, 02, 01, 11, 10, 00 (1.1)is a cyclic 2-digit ternary Gray code. We only consider cyclic codes here.In the mid-twentieth century Frank Gray [7] designed...

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Báo cáo toán học: "Some cyclic solutions to the three table Oberwolfach problem" pptx

... 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 toOP(r, r, s) for ... ≤ 8. Table 2 of [12] gives cyclic solutions for all s inthe range 5 ≤ s ≤ Nr,whereNris taken from Table 1.For r in the range 9 ≤ r ≤ 13, Table 2 of [12] gives cyclic solutions for 5 ≤ s ... 11 −References[1] B.A. Anderson. Sequencings of dicyclic groups II. J. Combin. Math. Combin. Comp.,3:5–27, 1988.[2] B. A. Anderson. All dicyclic groups of order at least 12 have symmetric sequencings.Contemp....

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Báo cáo toán học: "The Cyclic Sieving Phenomenon for Faces of Cyclic Polytope" docx

... Inthis 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 thatcyclically 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 ndC a ﬁnite cyclic group acting on X. The triple (X, X(q), C) is said to exhibit the cyclic sieving ... Eq. (2), and let C = Znact on X by cyclic translation of the vertices. Then the triple (X, X(q), C) exhibits the cyclic sievi ngphenomenon.For odd d, the cyclic g r oup C is not an automorphism...