Báo cáo toán học: "Symmetric Simplicial Pseudoline Arrangements" ppsx

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Ngày tải lên: 05/08/2014, 09:46

... square-counting or an interlacing argument, one can show that the max- imum number of vertices in an independent set in the Hoffman-Singleton graph is 15. If S is an independent set of size 15 in this ... Then H is the Hoffman-Singleton graph. Note that we may view the vertices in S as points and the vertices not in S as lines, with a point and line incident if the corresponding verti...

Ngày tải lên: 07/08/2014, 06:20

... and the second follows from (2) and the bounds for R 5 (3) given in S. Radziszowski’s survey paper [6]. For earlier work on lower bounds for S(k) see H. Fredricksen [5] and A. Beutelspacher and W. ... D k (n)tobethemaximumofD(P )overall symmetric sum-free partitions P of [1,n]intok sets. Notethatwemusthave D k (n) ≤ S(k − 1) + 1. Symmetric Sum-Free Partitions...

Ngày tải lên: 07/08/2014, 06:20

... 3 q }. This coloring is easy to show not to have any rainbow arithmetic progressions of length at least 3. It turns out that in order to force a rainbow AP(k) we need to ensure that for each color ... A 5 and i is odd, C otherwise. (4) the electronic journal of combinatorics 11 (2004), #R1 6 On rainbow arithmetic progressions Maria Axenovich Department of Mathematics Iowa State Uni...

Ngày tải lên: 07/08/2014, 08:20

... symbol of σ.Sincen +1>m, we can select a random subsequence of σ of length m by first throwing out one of the n + 1 symbols of σ at random and then randomly selecting a subsequence of length ... the following theorem of Stromquist. We give a proof which is somewhat shorter than the proof in [1], both for its own interest and because we will reuse the method of proof when stu...

Ngày tải lên: 07/08/2014, 08:22

... 05A05, 05C30 Abstract We show that matchings avoiding a certain partial pattern are counted by the 3- Catalan numbers. We give a characterization of 12312 -avoiding matchings in terms of restrictions ... decompose a 12312 -avoiding matching into smaller 12312 -avoiding matchings. For notational convenience, we denote by E j the edge (i, j) with i < j. Lemma 2.1 Let M be a 12312 -avo...

Ngày tải lên: 07/08/2014, 13:21

... of symmetric simplicial pseudoline arrangements constructed from the mirrors of a regular k-gon and three additional symmetry classes of pseudolines. Finally, Section 6 discusses symmetric simplicial pseudoline ... of simplicial pseudoline arrangements (also alluded to in [7]), but details of these families have not been published. This paper will produce several infinite families...

Ngày tải lên: 07/08/2014, 15:22

... proof of Theorem 28 of [4] can also be adapted to hereditary properties of tour- naments, to produce many properties with different exponential speeds, but we spare the reader the details. Of ... proof of Theorem 1. Lemma 7. Let P be a hereditary property of tournaments. If B(P) = ∞, then P contains arbitrarily large structures of Type 1 or 2. Proof. Let P be a hereditary pro...

Ngày tải lên: 07/08/2014, 15:23

... set X of b − 1 vertices, each of degree n − 1, a clique L of p 2 vertices, a the electronic journal of combinatorics 15 (2008), #R118 7 Saturation Numbers of Books Guantao Chen ∗ Dept. of Math. ... has a set X of b−1 vertices, each of degree n − 1, a clique L of p 2 vertices, a set T of n − p/2 − b + 1 vertices inducing an almost (p − 1)-regular graph which contains a v...

Ngày tải lên: 07/08/2014, 21:20

... [KT86] Ta ble 2: Saturation Numbers for Trees of Order 7 Question 2: Can sharper bounds be established for Theorems 12 , 1 3, 16-19? Question 3: For those classes of trees for which the saturation ... number. Specifically, trees with long induced paths will have saturation numbers near the minimum and trees with high values for δ 2 (T ) will have high saturation...

Ngày tải lên: 08/08/2014, 01:20

... 1 A k R k,k+1  1 k  A k , the electronic journal of combinatorics 16 (2009), #R128 3 Symmetric functions for the generating matrix of the Yangian of gl n (C) Natasha Rozhkovskaya Department of Mathematics Kansas ... to the terms of the sum, we conclude that each of them has the form (−1) m−k− 1 e k (u)p − m−k (u − k), and the Newton’s formula for eleme...

Ngày tải lên: 08/08/2014, 01:20

... orienta tion. 4 Coxeter elements A Coxeter word has one instance of each letter, so it defines an acyclic orientation of the Coxeter graph. This orientation is in fact well defined by the Coxeter element, ... a corresponding Coxeter word. So, Coxeter elements correspond bijectively to acyclic edge orientations of the Coxeter graph. And we have seen that moving the first lette...

Ngày tải lên: 08/08/2014, 01:20

... divisor of p n − 1. If (v − 1)/q ≡ 0 (mod 12), then there is no bowtie decomposition of K v which is invariant with respect to G. Proof. We identify the vertices of the complete graph with the elements ... 1. The coset G − ρ consists of the permutations on Z v of the form x → −x + i + 1. Each element o f G − ρ is a reflection about the axis passing through th...

Ngày tải lên: 08/08/2014, 12:22

... 4.1 Each of the constructions in Definitions 4.1 and 4.2 has the property that if the graph G satisfies the Laman conditions, then so does  G. This follows from Theorems 2.2 and 2.3 and the fact ... − 4. the electronic journal of combinatorics 17 (2010), #R154 39 proofs of the corresponding Laman- type t heorems for the groups C 2 and C s . The Laman- type...

Ngày tải lên: 08/08/2014, 12:23

... something of the form λr with λ > 1 3 . To see this, consider the following sequence of graphs H r (d) as d tends to infinity: the electronic journal of combinatorics 18 (2011), #P88 5 Growth of graph ... increase in the number of edges of the cube of a regular, co nnected graph. Such an increase was already demonstrated by Hegarty in Theorem 2. Here we give an alternativ...

Ngày tải lên: 08/08/2014, 14:23