منابع مشابه
Adjacencies in Words
Based Based on on two two inversion inversion formulas formulas for for enumerating enumerating words words in in the the free free monoid monoid by by adjacencies, adjacencies, we we present present a a new new approach approach to to a a class class of of permutation permutation problems problems having having Eulerian-type Eulerian-type generating generating functions. functions. We We also ...
متن کاملRestricted words by adjacencies
A recurrence, a determinant formula, and generating functions are presented for enumerating words with restricted letters by adjacencies. The main theorem leads to re nements (with up to two additional parameters) of known results on compositions, polyominoes, and permutations. Among the examples considered are (1) the introduction of the ascent variation on compositions, (2) the enumeration of...
متن کاملAdjacencies in Permutations
A permutation on an alphabet $ \Sigma $, is a sequence where every element in $ \Sigma $ occurs precisely once. Given a permutation $ \pi $= ($\pi_{1} $, $ \pi_{2} $, $ \pi_{3} $,....., $ \pi_{n} $) over the alphabet $ \Sigma $ =$\{ $0, 1, . . . , n$-$1 $\}$ the elements in two consecutive positions in $ \pi $ e.g. $ \pi_{i} $ and $ \pi_{i+1} $ are said to form an \emph{adjacency} if $ \pi_{i+1...
متن کاملRelative Adjacencies in Spatial Pseudo-Partitions
Introduction Qualitative spatial reasoning is a valid support for inferring relationships in geographical spaces. In particular, qualitative inferences are cognitively more expressive than quantitative ones, and support reasoning mechanisms in the absence of complete spatial knowledge (Cohn 1997). In geographical space, reasoning on spatial entities is supported by representations that mainly i...
متن کاملOptimizing Spatial Adjacencies Using Evolutionary Parametric Tools
This article documents the use of Grasshopper and Galapagos (Rhino plugins) as analytical tools to graphically represent and optimize the adjacency requirements in programmatic spaces. The resulting three-dimensional spatial diagrams are evaluated based on evolutionary fitness, which within this research context is defined as minimizing the numerical value of the total distance of all interconn...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1995
ISSN: 0196-8858
DOI: 10.1006/aama.1995.1010