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5 papers · 2 filters
On pattern avoiding indecomposable permutations
Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
Comtet introduced the notion of indecomposable permutations in 1972. A permutation is indecomposable if and only if it has no proper prefix which is itself a permutation. Indecompo…
Algorithm on rainbow connection for maximal outerplanar graphs
Xingchao Deng, Hengzhe Li, Guiying Yan
In this paper, we consider rainbow connection number of maximal outerplanar graphs(MOPs) on algorithmic aspect. For the (MOP) , we give sufficient conditions to guarantee that $…
The unimodality of the Ehrhart -polynomial of the chain polytope of the zig-zag poset
Herman Z. Q. Chen, Philip B. Zhang
We prove the unimodality of the Ehrhart -polynomial of the chain polytope of the zig-zag poset, which was conjectured by Kirillov. First, based on a result due to Stanley, we sh…
The Real-rootedness of Generalized Narayana Polynomials
Herman Z. Q. Chen, Arthur L. B. Yang, Philip B. Zhang
In this paper, we prove the real-rootedness of two classes of generalized Narayana polynomials: one arising as the -polynomials of the generalized associahedron associated to th…
On 132-representable Graphs
Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
A graph is word-representable if there exists a word over the alphabet such that letters and alternate in if and only if is an edge in . Wor…