147 research outputs found
Bounds for D-finite closure properties
We provide bounds on the size of operators obtained by algorithms for
executing D-finite closure properties. For operators of small order, we give
bounds on the degree and on the height (bit-size). For higher order operators,
we give degree bounds that are parameterized with respect to the order and
reflect the phenomenon that higher order operators may have lower degrees
(order-degree curves)
Walks in the Quarter Plane with Multiple Steps
We extend the classification of nearest neighbour walks in the quarter plane
to models in which multiplicities are attached to each direction in the step
set. Our study leads to a small number of infinite families that completely
characterize all the models whose associated group is D4, D6, or D8. These
families cover all the models with multiplicites 0, 1, 2, or 3, which were
experimentally found to be D-finite --- with three noteworthy exceptions.Comment: 12 pages, FPSAC 2015 submissio
The computational challenge of enumerating high-dimensional rook walks
We provide guessed recurrence equations for the counting sequences of rook
paths on d-dimensional chess boards starting at (0..0) and ending at (n..n),
where d=2,3,...,12. Our recurrences suggest refined asymptotic formulas of
these sequences. Rigorous proofs of the guessed recurrences as well as the
suggested asymptotic forms are posed as challenges to the reader
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