Geodesic
The enumeration of sequences with restrictions on their partial sums
The electronic journal of combinatorics, Tome 17 (2010)

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Zbl EuDML
We examine sequences containing $p$ "$-t$"s and $pt+r$ "$+1$"s, where $p$, $t$, and $r$ are integers satisfying $p\ge0$, $t\ge 1$ and $pt+r\ge0$. We develop a rotation method to enumerate the number of sequences meeting additional requirements related to their partial sums. We also define downcrossings about $\ell$ and their downcrossing numbers, and obtain formulas for the number of sequences for which the sum of the downcrossing numbers equals $k$, for $\ell \le r+1$. We finish with an investigation of the first downcrossing number about $\ell$, for any $\ell$.
DOI : 10.37236/432
Classification : 05A15, 05A10
Mots-clés : lattice paths, ballot problem, rotation method, crossings, crossing sums, generalized binomial series, downcrossings, downcrossing number 
Stephen Suen; Kevin P. Wagner. The enumeration of sequences with restrictions on their partial sums. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/432
@article{10_37236_432,
     author = {Stephen Suen and Kevin P. Wagner},
     title = {The enumeration of sequences with restrictions on their partial sums},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/432},
     zbl = {1204.05016},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/432/}
}
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