Báo cáo toán học: "Rationality, irrationality, and Wilf equivalence in generalized factor order" ppsx
Báo cáo toán học: "Mapping cones and exact sequences in KK-theory " pptx
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Báo cáo toán học: "Two new criteria for comparison in the Bruhat order" pot
... transpositions, then the poly-nomial (1) is equal to a sum of polynomials of the form (2) and again is TNN.(⇐) Suppose that π is not less than or equal to σ in the Bruhat order. By Theorem 1we ... transpositions, then the evaluation of (3) at A is equal to a sum of polynomials of the form (4) and again (3) isSNN.(⇐) Suppose that π is not less than or equal to σ in the Bruhat order. By Theorem ... Our second new criterion defines the Bruhat order in terms of Schur functions. (See[9, Ch. 7] for definitions.) Any finite submatrix of the in nite matrix H =(hj−i)i,j≥0,where hkis the kth...
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Báo cáo toán học: " Tight Quotients and Double Quotients in the Bruhat Order" doc
... hypotheses of the above claim are satised, and hence x(à) x().On the other hand, bearing in mind that à and are in the interior of the same Weylchamber C,andwà = à+ and w = +are dominant, we ... (Lemma 4.5) and the induction continues. For the numbering of the vertices of A0 in what follows, refer to Figure 4.Corollary 5.6. The Bruhat orderings of the double quotients (Bn.θ1)S, ... The (lack of) tight quotients in affine Weyl groups.Note that the standard ordering ofV generated byΦ induces partial orderings onany subset ofV , including the cross section X and the...
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Báo cáo toán học: "Grid classes and the Fibonacci dichotomy for restricted permutations" ppsx
... alternations either with blocks of the form π(k,+) for +>or of the form π(k,−) for −<, and horizontal alternations with blocks of the form π(k+,) for k+>kor of the form π(k−,) for ... than the nth Fibonacci number for some n .The definition of sub-2n−1is analogous. the electronic journal of combinatorics 13 (2006), #R54 9 Grid classes and the Fibonacci dichotomy for restricted ... Nt.Therefore Theorem 1.1 shows that Cρhas eventually polynomial enumeration, and so Cdoes as well.3 The Fibonacci dichotomy The Fibonacci dichotomy for permutation classes, first proved by Kaiser and...
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Báo cáo toán học: "Total domination and matching numbers in claw-free graphs" doc
... claw-free graphs with minimum degree atleast three that have equal total domination and matching numbers. Keywords: claw-free, matching number, total domination number1 IntroductionTotal domination ... graph G is a matching if no two edges in M are incidentto the same vertex. The matching number of G is the maximum cardinality of a matching of G.AsetS of vertices in G is a total dominating set ... 4-cycle containing both v1 and v2or containing both v3 and v4.Proof. Suppose, to the contrary, that there is a 4-cycle containing both v1 and v2orcontaining both v3 and v4. By symmetry,...
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Báo cáo toán học: "Distance domination and distance irredundance in graphs" ppsx
... generalizing a result of Favaron and Kratsch [4]regarding k = 1.Keywords: domination, irredundance, distance domination number, total domi-nation number, connected domination number, distance irredundance ... − D and D is at most k (and D induces aconnected graph in G). The minimum cardinality of a (connected) distance k-dominatingset in G is the (connected) distance k -domination number of G, denoted ... (connected) distance k-dominating setof G if the distance between each vertex u ∈ V − D and D is at most k (and D induces a connected graph in G). The minimum cardinality of a (connected)distance...
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Báo cáo toán học: "Global alliances and independent domination in some classes of graphs" pdf
... γ(G) and i(G) are respectively the minimum cardinality of a dominating set and of an independent dominating set and β(G) is the maximumcardinality of an independent set. Alliances are defined in ... corona of a graph is obtained byattaching a pendant edge at each vertex of G.the electronic journal of combinatorics 15 (2008), #R123 2 Global alliances and independent domination in some classes ... dS(v) and are all disjoint. Let J be anymaximal independent set of G[S] and q the number of components of the forest inducedby S \ J. The set I = Jv∈S\JL(v) is a maximal independent set of...
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Báo cáo toán học: "Topological circles and Euler tours in locally finite graphs" pptx
... containing a finite odd cut of Gextends to an element of C.1 IntroductionErd˝os et al. [17] characterised the in nite graphs G containing an Euler tour, that is, atwo-way in nite walk traversing ... ny arc in |G| with on e endpoint in X and one in Y contains an edge from F .4 Euler tours In this section we prove Theorem 1.3, but before we do so let us consider an example indi-cating why, ... applications in the study of hamil-tonicity in infinite graphs. If G is a locally finite graph then we define a Hamilton circleof G to be a circle in |G| containing all vertices (and hence also...
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Báo cáo toán học: "Rationality, irrationality, and Wilf equivalence in generalized factor order" ppsx
... of the embedding factor w′= 343 which has embedding index 5, and the two 2’s of u are in po sitions 6 and 7. Note that we obtain ordinary factor order by taking P to be an antichain. Also, wewill ... explainsall the Wilf equivalences in S5. In particular, the results of Section 4 and the lastparagraph of Section 5 generat e all of the Wilf equivalences in Table 1 with one exception. In ... “weakly increasing” and “maximum” have their usual meanings. Also, let w+mbe the result of applying the+ operator m times. By using the previous lemma a nd induction, we obtain the followingresult....
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Báo cáo toán học: "Bootstrap Percolation and Diffusion in Random Graphs with Given Vertex Degree" pptx
... Diffusion of innovations on random networks: Understanding the chasm. In Proceedings of WINE 2 008, pages 178–185, 2008.[20] M. Molloy and B. Reed. A critical point for random graphs with a given ... the study of percolation in a random graph with given vertex degrees. We refer to Section 3 for more details.k-Core in Random Graphs with Given Degree Sequence. Let k 2 be a fixedinteger. The ... t) in the case of ra ndom graphs with g iven vertex degrees. The next section describes thismodel of ra ndom graphs. 1.1 Random Graphs with Given node Degrees In this paper, we investigate random...
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Báo cáo toán học: "Dry matter and nitrogen allocation in western redcedar, western hemlock, a" ppsx
... production and survival in thefield. High N concentrations in seedlings may lead to Original articleDry matter and nitrogen allocation in western redcedar, western hemlock, and ... balance and organic acids in western redcedar, western hemlock, and Douglas fir seedlings grown in low- and high-N soils, Can. J.For. Res. 29 (1999) 669-678.[16] Hawkins ... relative dry -matter increment(Loge(DMfinal) - Loge(DMinitial); RDMI) and relative N increment (Loge(Nfinal) - Loge(Ninitial); RNI) in each soil and accumulated35...
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Báo cáo toán học: " Exterior Pairs and Up Step Statistics on Dyck Paths" ppsx
... said to be exterior if τ(uv) contains at least two leaves. One can check tha t the exterior edges of Tare in one-to-one correspondence with the exterior pairs of the corresponding Dyck pathΛ−1(T ... nd a down step, respectively. In[3], Denise and Simion introduced and investigated the two statistics ‘pyramid weight’ and ‘number of exterior pairs on the set Cn. A pyramid in a Dyck path ... passed on the way up there corresponds a down step. For example,Figure 3 shows a Dyck path of length 14 with 2 blocks and the corresponding orderedtree.Figure 3: A Dyck path and the corresponding...
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Báo cáo toán học: "Permutation Tableaux and the Dashed Permutation Pattern 32–1" ppsx
... T and the permutation π obtained from T by the first bijection of Corteel and Nadeau, we prove that the inversionnumber of T equals the number of occurrences of the dashed pattern 32–1 in the ... 0equals Bn.On the other hand, the following relation was proved by Corteel and Nadeau [7].Theorem 3.2. The number of L-Bell permutation tableaux of length n equals Bn.By the definition o ... avoiding the dashed pattern 32–1 is given by the n- t h Bell number Bn. In view of Theorem 2.1,we are led to the following correspondence.Theorem 3.1. The number of permutation tableaux T...
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Báo cáo toán học: "Partitions, rooks, and symmetric functions in noncommuting variables" pdf
... Tevlin, L., Thibon, J Y.,Thiem, N., Venkateswaran, V., Vinroot, C. R., Yan, N., and Mike, Z.Supercharacters, symmetric functions in no ncommut ing variables, and related Hopfalgebras. Preprint ... Rosas, M., and Zabrocki, M. Invariants and coinvariants of t he symmetric groups in noncommuting variables. Canad. J.Math. 60, 2 (20 08), 266–296.[4] Chen, W. Y. C., Li, T. X. S., and Wang, ... easy to see that the maps R → πR and the electronic journal of combinatorics 18(2) (2011), #P3 2 Partitions, rooks, and symmetric functions in noncommuting variablesMahir Bilen CanDepartment...
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