The Enumeration of Election Returns by Number of Lead Positions
Riordan, John
Ann. Math. Statist., Tome 35 (1964) no. 4, p. 369-379 / Harvested from Project Euclid
In an election return with two candidates $A$ and $B$, if $\alpha_r$ is the number of votes for $A$ in the first $r$ counted, $\beta_r$ the similar number for $B$, then $r$ is a $c$-lead position for $A$ if $\alpha_r > \beta_r + c - 1$. With final vote $(n, m) (n$ for $A, m$ for $B$), what is the number $l_j(n, m; c)$ of returns with $j c$-lead positions? Or, what is the enumerator $l_{n m}(x; c) = \sum l_j(n, m; c)x^j$ of election returns by number of lead positions? For $c = 0, \pm 1, \pm 2, \cdots$ it is shown that all enumerators may be expressed in terms of $l_{n m}(x; 0)$ and $l_{n m}(x; 1)$, which are given explicit expression.
Publié le : 1964-03-14
Classification: 
@article{1177703760,
     author = {Riordan, John},
     title = {The Enumeration of Election Returns by Number of Lead Positions},
     journal = {Ann. Math. Statist.},
     volume = {35},
     number = {4},
     year = {1964},
     pages = { 369-379},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177703760}
}
Riordan, John. The Enumeration of Election Returns by Number of Lead Positions. Ann. Math. Statist., Tome 35 (1964) no. 4, pp.  369-379. http://gdmltest.u-ga.fr/item/1177703760/