Báo cáo toán học: "Reconstructing integer sets from their representation functions" pot

... Reconstructing integer sets from their representation functions Vsevolod F. Lev Department of Mathematics University of Haifa ... perfect difference sets A, B ⊆ G satisfy R (1) A = R (1) B . As a common generalization of the representation functions R (1) A and r A ,onecan consider two potentially different sets A, B ⊆ Z and ... large integer n with r A (n)=∞. On the other han...

Ngày tải lên: 07/08/2014, 08:22

... can be reconstructed from their multisets of cycle minors. 3 Application to Sequence Reductions Theorem 2.1 can be applied to the problem of reconstructing permutations from their sequence reductions. Definition. ... of combinatorics 16 (2009), #R19 7 cycle representation of p and subsequently subtracting 1 from any number that is between i and j and subtracting 2 from any number...

Ngày tải lên: 07/08/2014, 21:21

... singleton or doubleton set of positive integers is the score set of some tournament. Theorem 2. Let S = {s, sd, sd 2 , ,sd p },wheres and d are positive integers, d>1. Then, there exists a ... ,s+pd},wheres and d are n on-negative integers, d>0. Then, there is a tournament T such that S T = S. Theorem 4. Let S = {s, s + d, s + d + e},wheres, d,ande are non-negative integers and de >...

Ngày tải lên: 06/08/2014, 05:20

... two words are adjacent whenever their Hamming distance is not equal to afixed δ∈{ 1 , ,n} , then a pair of disconnected sets becomes an equidistant code pair . For disconnected sets A and B we will give ... ,6therespectivevaluesof Q 4,j are1,6, − 9, − 44,111, − 90and25.Theorem2.5givesφ 4 =46656/286 ≈ 163.13.WithLemma3.1(takeδ  =2)wefind45 √ 6 ≤ Φ 4 ≤ 23328/143. Thisexampleshowsthatourbou...

Ngày tải lên: 07/08/2014, 06:20

... consider the problem of reconstructing subsets of the groups ,  ,and from the multiset of isomorphism classes of their subsets of fixed size, where two subsets are isomorphic if one subset is a ... -linear combination of a finite set of elements from I. We will show that for finite subsets J with I 0 ⊂ J ⊂ I,thesetsA ∩J and B ∩J are equal, from which it easily follows that A = B.C...

Ngày tải lên: 07/08/2014, 06:20

... [6], we have shown that the designs corresponding to certain McFarland and Spence difference sets (or their complements) serve as such starters. In Section 3 of this paper, we show that for h = ... difference sets are known (see [3] or [7] for references). We will mention the McFarland family having parameters (p d+1 (r+1),p d r, p d−1 (r−1)), where p is a prime power, d is a p ositive i...

Ngày tải lên: 07/08/2014, 06:22

... 2q 2 = 2 9 (d+1) 2 vertices. From the standard procedure sketched earlier, we thus obtain an equiangular set of 2 9 (d +1) 2 lines in Euclidean d-space, whenever d =3q − 1=3· 2 2t−1 − 1 for some positive integer ... perhaps surprising that their relevance to equiangular lines was not noticed before. A likely reason is that, generally speaking, the best constructions seem to come from...

Ngày tải lên: 07/08/2014, 06:22

... certain sets of integers, J. London Math. Soc. 28 (1953), 104-109. [7] K. Roth, On certain sets of integers, II , J. London Math. Soc. 29 (1954), 20-26. [8] E. Szemer´edi, On sets of integers ... diagram, {s 1 ,s 3 ,s 5 } is not a triangle in S.) 3.12 Definition. Let Y and W be sets, each with specified sets of “triangles”, i.e. three element subsets. A function σ : Y → W is a triangle...

Ngày tải lên: 07/08/2014, 06:23

... Conjecture 2 from [22] which was mentioned above. We deal with complexity questions related to feasible sets of mixed hypergraphs in Section 4. We prove that for any fixed finite sets of positive integers ... Feasible sets of mixed hypergraphs with maximum degree three need not to be gap-free. The feasible sets of planar mixed hypergraphs, i.e., hypergraphs whose bipartite incidence g...

Ngày tải lên: 07/08/2014, 08:20

... (right, from [7]). the zonohedron is the planar dual to the great circle arrangement, and its vertices and edges form a geometric representation of the cubic partial cube C A . However, this representation ... three-dimensional representations with sym- metric faces, most but not all of which are strictly convex, even for the graphs C A coming from pseudoline arrangements A. To do so,...

Ngày tải lên: 07/08/2014, 13:21