Geodesic
A well-rounded linear function
The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2
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The generic linear function $ax+b$ of a real variable, with $a, b, x \in {\bf R}$, is usually evaluated as a scale function (product) followed by a translation (sum). Our main result shows that when such a function is variously combined with rounding functions (floor and ceiling), exactly 67 inequivalent rounded generic linear functions result, of which 38 are integer-valued and 29 are not. Several related results are also established, with elucidation of the relevant equivalence class structures.
DOI : 10.37236/1605
Classification : 05A15, 11A99, 26A09
Mots-clés : composite functions, linear function, floor and ceiling function, equivalence classes 
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     author = {Roger B. Eggleton},
     title = {A well-rounded linear function},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {2},
     doi = {10.37236/1605},
     zbl = {0990.05005},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1605/}
}
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Roger B. Eggleton. A well-rounded linear function. The electronic journal of combinatorics, The Fraenkel Festschrift volume, Tome 8 (2001) no. 2. doi: 10.37236/1605

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