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16 papers · 2 filters
Proof of the Somos-4 Hankel Determinants Conjecture
Guoce Xin
By considering the fundamental equation , Somos conjectured that the Hankel determinants for the generating series are the Somos-4 numbers. We prove this conj…
Partitioning complete graphs by heterochromatic trees
Zemin Jin, Xueliang Li
A {\it heterochromatic tree} is an edge-colored tree in which any two edges have different colors. The {\it heterochromatic tree partition number} of an -edge-colored graph ,…
Lattice and Schroder paths with periodic boundaries
Joseph P. S. Kung, Anna de Mier, Xinyu Sun +1
We consider paths in the plane with and -steps that start at the origin, end at height and stay to the left of a given non-decreasing right boundary.…
Partial transpose of permutation matrices
Qing-Hu Hou, Toufik Mansour, Simone Severini
The partial transpose of a block matrix M is the matrix obtained by transposing the blocks of M independently. We approach the notion of partial transpose from a combinatorial poin…
The Limiting Distribution of the Coefficients of the -Catalan Numbers
William Y. C. Chen, Carol J. Wang, Larry X. W. Wang
We show that the limiting distributions of the coefficients of the -Catalan numbers and the generalized -Catalan numbers are normal. Despite the fact that these coefficients…
The Ratio Monotonicity of the -Derangement Numbers
William Y. C. Chen, Ernest X. W. Xia
We show that the -derangement numbers satisfy a ratio monotone property, which is analogous to the log-concavity and is stronger than the spiral property and the unimodality.