Báo cáo toán học: "Face numbers and nongeneric initial ideals" doc

... J. Herzog, and T. Hibi. Shifting operations and graded Betti numbers. J. Algebraic Combin., 12:207–222, 2000. [3] D. Bayer, H. Charalambous, and S. Popescu. Extremal Betti numbers and applica- tions ... parts 1 and 2 are [11, Lemma 6.3], and part 3 follows from Corollary 2.5 and Lemma 2.6 of [2]. In the rest of this section we discuss an application of Lemma 2.2 to the face...

Ngày tải lên: 07/08/2014, 08:22

... .) Theorem 2. Let n ≥ 2, and le t a, b be words such that (a, b) ∈ S n−1 . Then the word (n+2, a, n, b, n+1) ∈ S n+2 is a primi tive G-word if and only i f 1 ∈ b and both (n+1, a ∗ , n) and (n + 1, b, ... and let P, Q be subsets of [n] such that p = |P | ≥ 3, q = |Q| ≥ 3, P ∪ Q = [n], and P ∩ Q = {n − 2}. Let x = (x 1 , a, x p ) ∈ S P and y = (y 1 , b, y q ) ∈ S Q such that x p...

Ngày tải lên: 07/08/2014, 21:21

... T i for some i. Let u and v be the hub vertices of T and let Q 1 , Q 2 and Q 3 be the paths of T ea ch containing u and v. Suppose u and v are each incident to at least one edge of E and, without loss ... T i for some i. Let u and v be the hub vertices of T and let Q 1 , Q 2 , Q 3 be the three paths of T , each including u and v. Suppose u and v are each incident to at leas...

Ngày tải lên: 08/08/2014, 14:23

... either four or five numbers. If A 2 covers four numbers, then A 3 ,A 5 and A 7 can cover not more than two numbers, one number, and one number, respectively, out of five remaining numbers, thus, leaving ... coverings, and to Prof. Lev B. Levitin for useful discussions and comments. Special thanks are due to the referee for carefully reading the paper and suggesting thoughtful imp...

Ngày tải lên: 07/08/2014, 06:20

... the definitions of the small and large Schr¨oder numbers (as seen in [24]): Let the small and large d-Schr¨oder numbers, respectively, be the sequences (N d,n (2)) n≥1 and (2 d−1 N d,n (2)) n≥1 , ... i<dn}|. Define the matrices M A and M D so (M A ) j := 1 if j<, and = 0 if otherwise, (M D ) j := 1 if j>, and = 0 if otherwise. Hence, asc(P )=Θ M A (P ) and des(P )=...

Ngày tải lên: 07/08/2014, 08:20

... φ O and φ X\O . Consequently g is in the subgroup Stab(O) ∩ Stab(X\O)andsog is in Stab(X). This gives a numerical condition for 2-distinguishability. Corollary 2.4. Suppose Γ acts on X and O 1 and ... x 1 ∈ O 1 and x 2 ∈ O 2 . Define a labelling φ : X −→ { 1, 2} by setting φ(x 1 )=φ(x 2 )= 2and (x) = 1 for all other x.Ifg preserves φ then it satisfies φ(g.x 1 )=2=φ(g.x 2 ). Since g.x i...

Ngày tải lên: 07/08/2014, 08:20

... Factors and Factorization. 403–430. Handbook of Graph Theory ed. J. L. Gross and J. Yellen. CRC Press, 2003, ISBN: 1-58488-092-2. [11] W. R. Pulleyblank, Matchings and Extension. 179–232. Handbook ... journal of combinatorics 13 (2006), #R59 9 Total domination and matching numbers in claw-free graphs 1 Michael A. Henning ∗ and 2 Anders Yeo 1 School of Mathematical Sciences Univers...

Ngày tải lên: 07/08/2014, 13:21

... and fix(Γ) = {1, . . . , k}. 3.2 Symmetric groups The inflation of a graph G, Inf(G), is a graph with a vertex for each ordered pair (v, e), where v and e are a vertex and an edge of G, and v and ... that v and u are adjacent vertices of Inf k (K n ). By the definition of inflatio n, v = (v ′ , e ′ ) and u = (u ′ , d ′ ) for two vertices v ′ and u ′ in Inf k−1 (K n ) and two edg...

Ngày tải lên: 07/08/2014, 21:21

... counted by the Fibonacci numbers. These distribu- tions will give us q-Fibonacci numbers which are related to the q-Fibonacci numbers of Carlitz [2], Cigler [3, 4], and Goyt and Sagan [6]. Let the ... where F n = F n−1 + F n−2 and F 0 = 1 and F 1 = 1. Let [n] = {1, 2, . . . n} and [k, n] = {k, k + 1, . . . , n}. We will call two integer sequences a 1 a 2 . . . a k and b 1 b 2...

Ngày tải lên: 08/08/2014, 01:20

... plane, 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 ... Eliahou and Kervaire [15] and Aramova, Herzog, and Hibi [1]. The answers for I(F ) generalize Corollary 2.17. Corollary 3.14 If K is a squarefree strongly stable d-uniform hypergraph,...

Ngày tải lên: 08/08/2014, 01:20