Alphabetic points in compositions and words
-
Margaret Archibald
,
Aubrey Blecher
Abstract
We use generating functions to account for alphabetic points (or the lack thereof) in compositions and words. An alphabetic point is a value j such that all the values to its left are not larger than j and all the values to its right are not smaller than j. We also provide the asymptotics for compositions and words which have no alphabetic points, as the size tends to infinity. This is achieved by the construction of upper and lower bounds which converge to each other, and in the latter case by probabilistic arguments.
Originally published in Diskretnaya Matematika (2021) 33,№2, 20–30 (in Russian).
Funding statement: This material is based uponwork supported by the National Research Foundation under grant numbers 89147, BLEC 018 and 81021 respectively
Acknowledgment
The authors would like to thank the reviewer for a careful reading of the manuscript and a simplification of the improved upper bound in Subsection 2.4.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On closed classes in partial k-valued logic that contain all polynomials
- Alphabetic points in compositions and words
- Medial strongly dependent n-ary operations
- Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping
- Implementation complexity of Boolean functions with a small number of ones
- Large deviations of branching process in a random environment
- Local limit theorems for generalized scheme of allocation of particles into ordered cells
Articles in the same Issue
- Frontmatter
- On closed classes in partial k-valued logic that contain all polynomials
- Alphabetic points in compositions and words
- Medial strongly dependent n-ary operations
- Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping
- Implementation complexity of Boolean functions with a small number of ones
- Large deviations of branching process in a random environment
- Local limit theorems for generalized scheme of allocation of particles into ordered cells
