The site-perimeter of compositions
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Aubrey Blecher
,
Charlotte Brennan
Abstract
Compositions of n are finite sequences of positive integers
We represent a composition of n as a bargraph with area n such that the height of the i-th column of the bargraph equals the size of the i-th part of the composition. We consider the site-perimeter which is the number of nearest-neighbour cells outside the boundary of the polyomino. The generating function that counts the total site-perimeter of compositions is obtained. In addition, we rederive the average site-perimeter of a composition by direct counting. Finally we determine the average site-perimeter of a bargraph with a given semi-perimeter.
Note: Originally published in Diskretnaya Matematika (2022) 34,№1, 3–19 (in Russian).
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Funding: The work of Charlotte Brennan was supported by the National Research Foundation under grant number 86329. The work of Arnold Knopfmacher was supported by the National Research Foundation under grant number 81021.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- The site-perimeter of compositions
- Some cardinality estimates for the set of correlation-immune Boolean functions
- Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate
- Completeness criterion with respect to the enumeration closure operator in the three-valued logic
- Some families of closed classes in Pk defined by additive formulas
- Finding periods of Zhegalkin polynomials
- Admissible and Bayes decisions with fuzzy-valued losses
Articles in the same Issue
- Frontmatter
- The site-perimeter of compositions
- Some cardinality estimates for the set of correlation-immune Boolean functions
- Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate
- Completeness criterion with respect to the enumeration closure operator in the three-valued logic
- Some families of closed classes in Pk defined by additive formulas
- Finding periods of Zhegalkin polynomials
- Admissible and Bayes decisions with fuzzy-valued losses
