Kitaev, Sergey and McAllister, Tyrrell and Petersen, T. Kyle (2006) Enumerating segmented patterns in compositions and encoding with restricted permutations. Integers: Electronic Journal of Combinatorial Number Theory, 6. ISSN 1553-1732Full text not available in this repository. (Request a copy from the Strathclyde author)
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of occurrences of arbitrary segmented partially ordered patterns among compositions of n with a prescribed number of parts. These patterns generalize the notions of rises, drops, and levels studied in the literature. We also obtain results enumerating parts with given sizes and locations among compositions and palindromic compositions with a given number of parts. Our results are motivated by “encoding by restricted permutations,” a relatively undeveloped method that provides a language for describing many combinatorial objects. We conclude with some examples demonstrating bijections between restricted permutations and other objects.
|Keywords:||segmented patterns, palindromic compositions, bijections, Electronic computers. Computer science|
|Subjects:||Science > Mathematics > Electronic computers. Computer science|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||14 Oct 2014 13:45|
|Last modified:||20 Apr 2017 00:08|