Báo cáo toán học: "Counting Lattice Paths by" potx

... August 3, 2000AbstractLet d(n) count the lattice paths from (0, 0) to (n, n) using the steps (0,1),(1,0), and (1,1). Let e(n) count the lattice paths from (0, 0) to (n, n)withpermitted steps ... of lattice paths deﬁned on various sets of permitted steps which yield pathcounts related to the Narayana polynomials.Mathematical Reviews Subject Classiﬁcation: 05A15Key words: Lattice paths, ... bijection f for these paths in Figures 1d and 1e. (We use“A = {1, 5}” in Section 4. )For the step set, S3= {V, H,D},whereD =(1, 1), the paths of L3(n)areknownas large Schr¨oder paths since |L3(n)|...

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Báo cáo toán học: "Counting set systems by weight" doc

... set, Fibonacci Quart.,19 (1981), 463–465.[12] R. Simion and D. Ullman, On the structure of the lattice of noncrossing parti-tions, Discrete Math., 98 (1991), 193–206.[13] N.J.A. Sloane (2000), ... for some block A of P and there is no z ∈ A with x<z<y.Thecomponents of G are increasing paths corresponding to the blocks of P .Equivalently,Ghas the property that each vertex has degree...

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Báo cáo toán học: "Counting peaks and valleys in k-colored Motzkin paths" doc

... Deutsch, A bijection on Dyck paths and its consequences, Discrete Math. 179(1998), 253–256 (Corrigendum: 187 (1998), 297).[6] E. Deutsch, An involution on Dyck paths and its consequences, Discrete ... (resp. high valleys) in Dyck paths [7].We note that from Propositions 3.1 (ii), 3.6 and 5.1 we obtain the following result,which is well-known in the case of Dyck paths [6].the electronic journal ... above result. For this we need thefollowing lemma which extends a result for Dyck paths [12]tok-colored Motzkin paths. Lemma 5.4 For each i ∈ N there exists an involution ψiof M such thatpi+2(u)=vi(ψi(u))where...

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Báo cáo toán học: "Counting segmented permutations using bicoloured Dyck paths" pptx

... number of nonnegative lattice paths from (0, 0)to (n + k, n −k). Thus, the ﬁrst claim of the proposition is that |B[1]n,k| equals the numberof nonnegative lattice paths from (0, 0) to (2n, ... in terms of lattice paths we deﬁne the height of a step ina (bicoloured) lattice path as the height above the x-axis of its left point. Then B[h]isthe set of bicoloured Dyck paths whose red ... of the second part we consider the set of all lattice paths from(0, 0) to (2n, 0). Let Pnbe the language over {u, d} obtained from these2nn paths viathe usual coding, and let P = ∪n≥0Pn....

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Báo cáo toán học: "Counting Bordered Partial Words by Critical Positions" ppt

... connections have been made, in particular, with problems concerning primitive setsof integers, lattices, vertex connectivity in graphs, etc [4].Primitive partial words were introduced by Blanchet-Sadri...

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Báo cáo toán học: "Counting words by number of occurrences of some patterns" pps

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Báo cáo toán học: "Counting distinct zeros of the Riemann zeta-function" docx

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Báo cáo toán học: "Counting two-graphs related to trees" ppt

... Naz. Lincei, Roma, 1977.10. J. J. Seidel and S. V. Tsaranov, Two-graphs, related groups and root lattices, Bull.Math.Soc.Belg.42 (1990), 695–711.11. N. J. A. Sloane, A Handbook of Integer Sequences, ... two-graphs.Construction 1. Let T beatreewithedgesetX.LetV be the set of 3-subsets of X notcontainedinpathsinT .Then(X, V ) is a two-graph.Proposition 1.1. A two-graph arises from a tree by Construction ... select one, and call the colours black and white. Let V consist of all 3-subsetsof X such that the paths joining these vertices meet at a black vertex. Then (X,V )isatwo-graph. (If we use the other...

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Báo cáo toán học: "Counting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs" ppt

... proved that thenumbers bncount (i) (n − 1)-element sets X of plane lattice point in which each pointis connected to (0, 0) by a lattice path that makes steps only (0, 1) and (1, 0) and liescompletely ... relations, Q. J. Math., Oxf. II 31 (1980), 491–506.[19] L. W. Shapiro, Directed animals and Motzkin paths, manuscript 1999.the electronic journal of combinatorics 7 (2000), #R34 25[20] M. Sharir...

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Báo cáo toán học: "Counting Simplexes in R 3" ppt

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