Durfee squares in compositions
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Margaret Archibald
Abstract
We study compositions (ordered partitions) of n. More particularly, our focus is on the bargraph representation of compositions which include or avoid squares of size s × s. We also extend the definition of a Durfee square (studied in integer partitions) to be the largest square which lies on the base of the bargraph representation of a composition (i.e., is ‘grounded’). Via generating functions and asymptotic analysis, we consider compositions of n whose Durfee squares are of size less than s × s. This is followed by a section on the total and average number of grounded s × s squares. We then count the number of Durfee squares in compositions of n.
Originally published in Diskretnaya Matematika (2018) 30, №3, 3–13 (in Russian).
funding
This material is based uponwork supported by the National Research Foundation under grant numbers 89147, 86329 and 81021.
References
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
Articles in the same Issue
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
