The run transform
Copyright policy )The run transform
We consider the transform from sequences to triangular arrays defined in terms of generating functions by f(x) -> (1-x)/(1-xy) f(x(1-x)/(1-xy)). We establish a criterion for the transform of a nonnegative sequence to be nonnegative, and we show that the transform counts certain classes of lattice paths by number of "pyramid ascents", as well as certain classes of ordered partitions by number of blocks that consist of increasing consecutive integers.
18 pages
- University of Wisconsin–Oshkosh United States
- New York University United States
- University of Wisconsin–Madison United States
- UNIVERSITY OF WISCONSIN-MADISON United States
Increasing run, Exact enumeration problems, generating functions, noncrossing partition, Theoretical Computer Science, Noncrossing partition, Partitions of sets, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Dyck path, Combinatorics (math.CO), pyramid ascent, Pyramid ascent, increasing run, 05A15
Increasing run, Exact enumeration problems, generating functions, noncrossing partition, Theoretical Computer Science, Noncrossing partition, Partitions of sets, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Dyck path, Combinatorics (math.CO), pyramid ascent, Pyramid ascent, increasing run, 05A15
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