منابع مشابه
A note on triangle partitions
Koivisto studied the partitioning of sets of bounded cardinality. We improve his time analysis somewhat, for the special case of triangle partitions, and obtain a slight improvement.
متن کاملNote On 1-Crossing Partitions
of Kirkman (first proven by Cayley; see [7]) for the number of dissections of an n-gon using d diagonals. The goal here is to generalize Bóna’s result to count 1-crossing partitions by their number of blocks, and also to examine a natural q-analogue with regard to the cyclic sieving phenomenon shown in [8] for certain q-Catalan and q-Narayana numbers. The crux is the observation that 1-crossing...
متن کاملA Note on Modular Partitions and Necklaces
Following Jens Voß [9], let T (n, k) be the number of k-tuples u = (u1, u2, . . . , uk) with 0 ≤ u1 ≤ u2 ≤ · · · ≤ uk ≤ n− 1 such that ∑ j uj ≡ 0 mod n. Stated another way, T (n, k) is the number of ways to write 0 as a sum of k elements of Z/nZ. Voß calls u a modular partition of n into k parts. He computed the numbers T (n, k) for n+ k ≤ 20, and part of his table is shown here (the rows corre...
متن کاملA note on random walks in a hypercube
We study a simple random walk on an n-dimensional hypercube. For any starting position we find the probability of hitting vertex a before hitting vertex b, whenever a and b share the same edge. This generalizes the model in [2] (see Exercise 1.3.7 there). Random walks, electric networks, hypercube 60G50, 60J45 Consider an n-dimensional hypercube, that is a graph with 2 vertices in the set {0, 1...
متن کاملA note on short cycles in a hypercube
How many edges can a quadrilateral-free subgraph of a hypercube have? This question was raised by Paul Erdős about 27 years ago. His conjecture that such a subgraph asymptotically has at most half the edges of a hypercube is still unresolved. Let f(n,Cl) be the largest number of edges in a subgraph of a hypercube Qn containing no cycle of length l. It is known that f(n,Cl) = o(|E(Qn)|), when l ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1973
ISSN: 0097-3165
DOI: 10.1016/0097-3165(73)90080-0