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20 papers · 2 filters
Loops in canonical RNA pseudoknot structures
Markus E. Nebel, Christian M. Reidys, Rita R. Wang
In this paper we compute the limit distributions of the numbers of hairpin-loops, interior-loops and bulges in k-noncrossing RNA structures. The latter are coarse grained RNA struc…
A Franklin Type Involution for Squares
William Y. C. Chen, Eric H. Liu
We find an involution as a combinatorial proof of a Ramanujan's partial theta identity. Based on this involution, we obtain a Franklin type involution for squares in the sense that…
Higher Order Log-Concavity in Euler's Difference Table
William Y. C. Chen, Cindy C. Y. Gu, Kevin J. Ma +1
Let be the entries in the classical Euler's difference table. We consider the array for , where can be interpreted as the num…
Minimally Intersecting Set Partitions of Type B
William Y. C. Chen, David G. L. Wang
Motivated by Pittel's study of minimally intersecting set partitions, we investigate minimally intersecting set partitions of type B. We find a formula for the number of minimally…
On Balanced Colorings of the n-Cube
William Y. C. Chen, Larry X. W. Wang
A 2-coloring of the n-cube in the n-dimensional Euclidean space can be considered as an assignment of weights of 1 or 0 to the vertices. Such a colored n-cube is said to be balance…
Note on the energy of regular graphs
Xueliang Li, Yiyang Li, Yongtang Shi
For a simple graph , the energy is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix . Let , respectively, be…