4 papers
Representing split graphs by words
Herman Z. Q. Chen, Sergey Kitaev, Akira Saito
There is a long line of research in the literature dedicated to word-representable graphs, which generalize several important classes of graphs. However, not much is known about wo…
On the probability of existence of a universal cycle or a universal word for a set of words
Herman Z. Q. Chen, Sergey Kitaev, Brian Y. Sun
A universal cycle, or u-cycle, for a given set of words is a circular word that contains each word from the set exactly once as a contiguous subword. The celebrated de Bruijn seque…
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…