تعداد نشریات | 43 |
تعداد شمارهها | 1,652 |
تعداد مقالات | 13,415 |
تعداد مشاهده مقاله | 30,702,944 |
تعداد دریافت فایل اصل مقاله | 12,121,278 |
Columns of fixed height in bargraphs | ||
Transactions on Combinatorics | ||
دوره 13، شماره 1، خرداد 2024، صفحه 67-84 اصل مقاله (525.97 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2023.132462.1957 | ||
نویسندگان | ||
Margaret Archibald* ؛ Aubrey Blecher؛ Arnold Knopfmacher | ||
The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050,Johannesburg, South Africa | ||
چکیده | ||
We obtain the generating function for the number of columns of fixed height $r$ in a bargraph (classified according to semi-perimeter). As initial case for two distinct methods we first find the generating function for columns of height $1$. Then using a first-return-to-level-$1$ decomposition, we obtain the rational function version of the continued fraction generating function which allows us to derive separate recursions for its numerator and denominator. This then allows us to get the asymptotic average number of columns for each $r$. We also obtain an equivalent generating function by exploiting a sequential decomposition for bargraphs in terms of columns of height $r$. | ||
کلیدواژهها | ||
generating function؛ bargraphs؛ column height | ||
مراجع | ||
[1] A. Blecher, C. Brennan, A. Knopfmacher and H. Prodinger, The height and width of bargraphs, Discrete Appl. | ||
آمار تعداد مشاهده مقاله: 99 تعداد دریافت فایل اصل مقاله: 136 |