Báo cáo toán học: "Shifted set families, degree sequences, and plethysm" potx

... for these values: m = 4, and k ≤ 7 m = 5, and k ≤ 6 m = 6, and k ≤ 4 m = 7, and k ≤ 4 m = 8, and k ≤ 3. Acknowledgments The authors thank Andrew Crites, Pedro Felzenszwalb and two anonymous referees ... electronic journal of combinatorics 15 (2008), #R14 30 Shifted set families, degree sequences, and plethysm C. Klivans ∗ Depts. of Mathematics and Computer Science, Uni...

Ngày tải lên: 07/08/2014, 15:23

... implies u ≺ v. First assume that π and π  differ only in two positions k and l with d  k = d k + 1 and d  l = d l −1 (and hence k < l and d k ≥ d l > 1). Let v k and v l be the corresponding ... vu /∈ P vx and ut /∈ E(G), then we set w = t. (2) Else, if vu /∈ P vx and ut ∈ E(G), then we set w to one of the neighbors of x that are not adjacent to u. (3) Else, if vu ∈...

Ngày tải lên: 07/08/2014, 21:20

... Signal Phase and Timing—SPAT, recommended speed and route guidance). There is, however, increasing inter- est in also supporting Internet communications from and to vehicles. By allowing classical and ... aware vehic- ular architecture standardized by ETSI, commonly referred to as geonetworking, and then describes in detail how IPv6 datagram transmission and standard IPv6 stateles...

Ngày tải lên: 20/06/2014, 20:20

... Decomposition Lemma, E 1 and E 2 partition {1, ,n−1}. Set S 1 =(s i :i∈E 1 ),S 2 =(s i :i∈E 2 )−s ∗ n . By part 3 of the Decomposition Lemma, S 1 and S 2 are major sequences of length l − 1andn−l, respectively, ... lemma. Recursively obtain the trees T 1 = f(S 1 )andT 2 =f(S 2 )on{0, ,l−1} and {0, ,n−l} respectively, with e(T 1 )=a(S 1 )ande(T 2 )=a(S 2 ), and thus by Part 4 of the...

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 05/08/2014, 15:21

... 140–146. [5] P. Erd ˝ os and R.L. Graham, Old and new problems and results in combinatorial number theory, L’Enseignement Math´ematique, Geneva, 1980. [6] V.F. Lev, Restricted set addition in groups. ... of a more general sort. Let A, B ⊆ G be subsets of a group G,andletR⊆A × B be any subset of the Cartesian product A × B. We define A R + B to be the set of all sums a + b, such that...

Ngày tải lên: 07/08/2014, 06:20

... series F (x) is denoted [x n ]F .Aset system H is here a finite multisubset of exp(N)whoseedges E ∈ H are nonempty and finite. The vertex set is V (H)=  E∈H E.Thedegree deg(x)=deg H (x) of a vertex ... The following definitions and Propositions 2.1 and 2.2 make this idea precise. We call two set partitions P and Q of [n] orthogonal if |A∩B|≤1 for every two blocks A ∈ P and B ∈ Q....

Ngày tải lên: 07/08/2014, 08:22

... ,d n )isthedegree sequence of G.Thedegree partition of G is obtained by rearranging d G in weakly decreasing order. Let DS(n)denotethesetofall degree sequences of simple graphs on the vertex set [n]andletDP(n)denotethesetof all ... the polytope of degree sequences, to be the convex hull (in R n )ofall degree sequences in DS(n) and define DP(n), the polytope of degree partitions,t...

Ngày tải lên: 07/08/2014, 13:21

... the X-multidegrees, setting the Y -multidegrees to 0, the two resolutions have exactly the same number of basis elements in each X-multidegree. The former is a resolution for S/I(G), and hence ... but rather inside the m × n rectangle with row and column indices given by X and Y . On the other hand, given a shifted skew diagram D, and a linearly ordered subset X, one can also form the...

Ngày tải lên: 08/08/2014, 01:20

... rooted at v and for every w ∈ V (T) the distance of v and w in T is the same as the distance of v and w in H. In ot her words, let T be a subtree of H rooted at v and let L i be the set of vertices ... p r−1 , 1 ≤ j ≤ p} (and their neighboring sets B i,j ) can be defined.  the electronic journal of combinatorics 18 (2011), #P108 3 of degree one and let v be any such vertex of G...

Ngày tải lên: 08/08/2014, 14:23