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Open Access research with a European policy impact...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the European Policies Research Centre (EPRC).

EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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Enumerating segmented patterns in compositions and encoding with restricted permutations

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 1553-1732

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Abstract

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.