Báo cáo toán học: "A combinatorial proof of Postnikov’s identity and a generalized enumeration of labeled trees" pdf

... electronic journal of combinatorics 11(2) (2005), #N3 3 A combinatorial pro of of Postnikov’s identity and a generalized enumeration of labeled trees Seunghyun Seo ∗ Department of Mathematics Brandeis ... left-hand (resp. right-hand) side of (2). The aim of this paper is to find a combinatorial proof of (2). In Section 2 we construct the sets F bi n of...

Ngày tải lên: 07/08/2014, 08:22

... article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. Random approximation with weak contraction random operators and a random fixed ... Beg and Shahzad [7] and many other authors have studied the fixed points of random maps. Choudhury [8], Park [9], Schu [10], and Choud- 2 Random approximation with weak contrac-...

Ngày tải lên: 20/06/2014, 21:20

... otherwise Breaker wins. A particular family of positional games originates from a seminal paper of Chv´atal and Erd˝os [4]. Let P be a monotone graph property. In the biased P-game Maker and Breaker are alternately ... Urbana, IL 61801, USA; and Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA. E-mail address: jobal...

Ngày tải lên: 08/08/2014, 14:22

... has been well studied; for a survey see [24]. Several years ago Thomassen asked if a planarity assumption and a distance constraint on P would help. Question 1 [21] Suppose G is a planar graph ... transforms G into H. Since deletion and contraction preserve planarity (and embeddability in any fixed surface), a planar graph cannot contain a K 5 minor since K 5 is not planar. Ho...

Ngày tải lên: 07/08/2014, 07:21

... journal of combinatorics 10 (2003), #R39 10 [6] J. Skokan and L. Thoma, Bipartite subgraphs and quasi-randomness, accepted to Graphs and Combinatorics. [7] E. Szemer´edi, Regular partitions of graphs, ... Lefmann and V. R¨odl, A fast algorithm for computing the frequencies of subgraphs in a given graph, SIAM J. Comp. 24 (1995), pp 598-620. [3] Y. Kohayakawa, V. R¨odl and J...

Ngày tải lên: 07/08/2014, 08:20

... y. Proof. As x and y are abelian, and a transitive abelian subgroup is regular [3, Theorem 4. 2A (v)], we have that fix x (B) and fix y (B) have order k and x/B, y/B are cyclic of order ... σ ∈ S m and, as y m ∈ P and y is abelian, we also have that y −1 z i y = z a i δ(i) for some δ ∈ S m and a i ∈ Z ∗ k . We conclude that both x and y normalize P , so t...

Ngày tải lên: 07/08/2014, 13:21

... define a random variable X A that we call a uniform random l ate choice from A by picking an element of  x⋆ A x uniformly at random. For notational convenience we define U (A, ) =  x⋆ A x . In ... A proof of the Kahn-Lov´asz theorem The entropy proof of the Kahn-Lov´asz theorem is complicated by the fact that there can be edges of the graph (and a fixed matching...

Ngày tải lên: 08/08/2014, 12:23

... bijections that map any pair of statistics (area, dinv), (dmaj, area  ), (pmaj, area) to any other. As a corollary, we obtain bijective proofs that all statistics in question have the same univariate ... obtain another combinatorial interpretation of the right side of formula (18) in which t keeps track of area and q keeps track of a new statistic pmaj.Asin§2, we can conclu...

Ngày tải lên: 07/08/2014, 08:20

... journal of combinatorics 15 (2008), #R45 7 An elementary proof of the hook formula Jason Bandlow ∗ Department of Mathematics University of California-Davis, Davis, CA, USA jbandlow@math.ucdavis.edu Submitted: ... (5) The proof of (3) is completely combinatorial, the proof of (4) uses nothing more than the fundamental theorem of algebra, and the proof of (5) is a s...

Ngày tải lên: 07/08/2014, 15:23

... LAR (m 2 g -1), was calculated as the ratio of total leaf area to total plant dry mass; specific leaf area, SLA (m 2 g -1), as the ratio of total leaf area to leaf ... and were separated into leaves, stem, and coarse (> 2 mm) and fine (< 2 mm) roots. Surface area of each leaf and total foliage area of each seedling were me...

Ngày tải lên: 08/08/2014, 14:21