75 citations · 402 across the 82 of their papers we have counts for
32 papers · 1 filter
Recurrences for permutations with long increasing subsequences
Manuel Kauers, Chen Wang
We prove two simple bivariate recurrences for the number of permutations with a long increasing subsequence. The two recurrences imply D-finiteness of the sequence in a certain ran…
On (3,1)-regular graphs with one more vertex than edges
Frédéric Chyzak, Hui Huang, Manuel Kauers
Sequence A339987 of the OEIS counts (3,1)-regular graphs having one more vertex than edges by half the number of vertices. A recurrence relation satisfied by this sequence was gues…
Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures
AJ Bu, Manuel Kauers, Doron Zeilberger
We derive precise asymptotic expressions for the expectations, variances, covariance, and quite a few further mixed moments for the number of hairpins and the number of basepairs i…
The Challenge of Computing Geode Numbers
Tewodros Amdeberhan, Manuel Kauers, Doron Zeilberger
In a fascinating recent American Mathematical Monthly article, Norman Wildberger and Dean Rubine introduced a new kind of combinatorial numbers, that they aptly named the ``Geode n…
The Asymptotic expansion of OEIS sequence A85
Shalosh B. Ekhad, Manuel Kauers, Doron Zeilberger
One of the most important sequences in enumerative combinatorics is OEIS sequence A85, the number of involutions of length n. In the Art of Computer Programming, vol. 3, Don Knuth…
Parallel Summation in P-Recursive Extensions
Shaoshi Chen, Ruyong Feng, Manuel Kauers +1
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that ra…