Tied dice. II. Some asymptotic results
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Abstract
- A dice family D(n,a,b,s) includes all lists (x1,…,xn) of integers with n≥1, a≤x1≤⋯≤xn≤b and Σxi=s. Given two dice X and Y we compare the number of pairs (i,j) with xi
yj. If the second number is larger than X is stronger than Y, and if the two numbers are equal then X and Y are tied. In previous work it has been observed that the density of ties in D(n,a,b,s) is generally lower than one might expect. In this note we provide more information about this observation by calculating the asymptotic proportion of ties in certain kinds of dice families. Many other properties of dice families remain to be determined.
| Title | Tied dice. II. Some asymptotic results |
|---|---|
| Creator | Gilson, E. |
| Follett, M. | |
| Ella, W. | |
| Traldi, Lorenzo | |
| Cooley, C. | |
| Publisher | Journal of Combinatorial Mathematics and Combinatorial Computing |
| Academic Department | Mathematics |
| Division | Natural Sciences |
| Organization | Lafayette College |
| Date Issued | 2014 |
| Date Available | 2017-06-26T17:29:57Z |
| Type | Article |
| Language | English |
| Bibliographic Citation | Cooley, C., et al. (2014) "Tied dice. II. Some asymptotic results." Journal of Combinatorial Mathematics and Combinatorial Computing 90 (2014): 241-8. |
| Standard Identifier | Handle 10385/2257 |
| Permalink | http://hdl.handle.net/10385/2257 |
| Rights Statement |
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| File | Traldi-JournalofCombinatorialMathematicsandCominatorialComputing-vol90-2014.pdf | Uploaded 2019-10-20 | Public | Download |
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