... August 3, 2000
Abstract
Let 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)with
permitted steps ... of lattice paths defined on various sets of permitted steps which yield path
counts related to the Narayana polynomials.
Mathematical Reviews Subject Classification: 05A15
Key words: La...
... 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.The
components of G are increasing paths corresponding to the blocks of P .Equivalently,G
has the property that each vertex has d...
... 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 elec...
... 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 number
of nonnegative lattice paths from (0, 0) to (2n, ... in terms of lattice paths we define the height of a step in
a (bicoloured) lattice path as the height above the x-axis of its left point. Then B
[h]
is
the set of bicoloured Dyck path...
... connections have been made, in particular, with problems concerning primitive sets
of integers, lattices, vertex connectivity in graphs, etc [4].
Primitive partial words were introduced by Blanchet-Sadri
... 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 not
containedinpathsinT .Then(X, V ) is a two-graph.
Proposition 1.1. A two-graph arises from a tree...
... proved that the
numbers b
n
count (i) (n − 1)-element sets X of plane lattice point in which each point
is connected to (0, 0) by a lattice path that makes steps only (0, 1) and (1, 0) and lies
completely ... 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 2...