Báo cáo toán học: "Betti numbers of monomial ideals and shifted skew shapes" potx

... one can check is not of the form G bip X,Y (D) for any shifted skew- shape D. However, one can still think of the edges of G as corresponding to the cells of a diagram in the shifted plane, which ... considered as drawn in the shifted 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 diagr...

Ngày tải lên: 08/08/2014, 01:20

... of the denominators of l 1 , , l r and the components of b.Then pc = kpl 1 a 1 + ···+ kpl r a r + kpb Vietnam Journal of Mathematics 34:4 (2006) 489–494 Integral Closures of Monomial Ideals and ... vector c ∈ N n is a vertex cover of order k of Δ if and only if M T ·c ≥ k1, where 1 denote the vector (1, , 1) of N m . By the above characterization of monomials of...

Ngày tải lên: 06/08/2014, 05:20

... Introduction and statement of main results In their study of connections between topology of order complexes and commutative al- gebra in [8], Bj¨orner and Welker introduced the notion of Rees product of ... the definition of the M¨obius function. For a ranked poset P of leng t h n and r ∈ {0, 1 , . . . , n}, let W r (P ) be the rth Whitney number of the second kind of...

Ngày tải lên: 08/08/2014, 01:20

... 1)y k +1. This completes the proof of (7) and verification of the upper bound. The proof of Theorem 1 is complete. Note that, by (7) and the remark following the proof of (6), all the orientations ... and o is alternating except for consecutive ↑’s in positions r − 1andr. the electronic journal of combinatorics 12 (2005), #R17 18 In each of (i) – (iii), and depending upon t...

Ngày tải lên: 07/08/2014, 08:22

... 7 Saturation Numbers of Books Guantao Chen ∗ Dept. of Math. and Stat. Georgia State University Atlanta, GA 30303 gchen@gsu.edu Ralph J. Faudree Dept. of Math. Sciences University of Memphis Memphis, ... combinatorics 15 (2008), #R118 12 (A). Let s 1 and s 2 ∈ S and let x 1 and x 2 be the corresponding neighbors in V 1 of s 1 and s 2 , respectively. If x 1 = x 2 and s...

Ngày tải lên: 07/08/2014, 21:20

... e), where v and e are a vertex and an edge of G, and v and e are incident. Inf(G) has an edge between (v 1 , e 1 ) and (v 2 , e 2 ) if v 1 = v 2 or e 1 = e 2 . We denote the k-fold inflation of the ... 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 ) a...

Ngày tải lên: 07/08/2014, 21:21

Ngày tải lên: 20/06/2014, 21:20

... by Noor [3–5] and Padmanabhan and Parvatham [2]. Also it can easily be seen that ( ) * 2 0 R S = and ( ) 2 0 , T K = where * S and K are the well-known classes of starlike and close-to-convex ... R: Properties of a class of functions with bounded boundary rotation. Ann. Polon. Math. 31, 311–323 (1975) [3]. Noor, KI: On radii of convexity and starlikeness of so...

Ngày tải lên: 20/06/2014, 21:20

... reached in the event of an average weekly consumption (median value) of, e.g. 1,795 g of chocolate and for children 772 g of chocolate. On the basis of the maximum aluminium content of chocolate, ... a weekly consumption of 467 g and for children of only 201 g. To reach the PTWI value of 70 mg per week (adults) and of 30 mg per week (children), the weekly consump...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:20