Báo cáo toán học: "Bicoloured Dyck paths and the contact polynomial for n non-intersecting paths in a half-plane lattic" pot

... journal of combinatorics 10 (2003), #R35 14 Bicoloured Dyck paths and the contact polynomial for n non-intersecting paths in a half-plane lattice. R. Brak† and J. W. Essam‡ ∗ †Department of Mathematics, The ... configurations of a single path starting at vertex v i α and ending at vertex v f β . The theorem may be used to find the Hankel n path contact...

Ngày tải lên: 07/08/2014, 08:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:20

... representatives. We will de- note the set of standard Catalan trees by standard(C) and the set of standard marked Catalan trees by standard(C, ∗). The standard trees in C 4 are , , , , . One of the ... weight function are met. An advantage to working with trees is that we can ignore the nature of the weights. On the other hand, perhaps we omit vital information when we do so...

Ngày tải lên: 07/08/2014, 06:22

... large and n ≡ d (mod c)} can be shown to form a fundamental antichain. Up to this point, all fundamental antichains in the literature and all antichains pro- duced by our algorithm as we have described ... 2), then the resulting antichain will not be fundamental. And if our stroll does not contain in nitely many cycles, then the resulting sequence of permutations will not e...

Ngày tải lên: 07/08/2014, 07:21

... that a  = (a 0 ,a 1 , ,a n ) is a member of the Catalan family. Since a is not in C we have a n = x and n +1= x.We consider two cases. If a n >xthen a  = (a 0 ,a 1 , ,a n 1 ,x)isnotinC and #{j ... from the relations g n = z n+ 1 and f n, r = z r z n r . Connection to other Catalan trees and objects It is well known that the Catalan num...

Ngày tải lên: 07/08/2014, 07:21

... m N . In the next section, using the generating function for the numbers µ r ,weobtainan expectation of the random variable ν = ν 2,1 for allocations at the second stage. To illus- trate our interest ... [2, 9] or in the singularity analysis [5], the most useful tools for obtaining asymp- totic expansions for the coefficients of generating functions. The saddle p...

Ngày tải lên: 07/08/2014, 07:21

... (4) There is an analogous equation for the second region on the right-hand side of (3), and the last term in (4) also appears in this. As we are considering parity, these terms cancel, leaving # 2 R ... determining the parity of the number of tilings of the region H(m, n) . In any tiling of H(m, n) , one particular domino must always be in place. In Figure 1(b), th...

Ngày tải lên: 07/08/2014, 08:22

... ∂Σ i if and only if there exist two maximal chains e old and e new , each containing e as a subchain, such that e old is a chain in X ∪ (  i−1 j=1 Σ j ) and e new is a chain in Σ i . Thus, ∂Σ i ⊆ ... chain in P i that is a lso a chain in P j for some j < i. Suppose that j is the least such integer, and consider the maximal chain c = Υ λ j (e). This chain ca...

Ngày tải lên: 08/08/2014, 12:23