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- Alice L. L. Gao, Emily X. L. Gao, Patxi Laborde-Zubieta, Brian Y. Sun
- Discrete Mathematics & Theoretical Computer…
- 2016

- Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
- Discrete Mathematics
- 2016

However, not much was understood on the structure of 123-avoiding up-down words. In this paper, we fill in this gap by introducing the notion of a cut-pair that allows us to subdivide the set of words in question into equivalence classes. We provide a combinatorial argument to show that the number of equivalence classes is given by the Catalan numbers,… (More)

- Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
- Australasian J. Combinatorics
- 2017

A graphG = (V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if xy is an edge in E. Word-representable graphs are the main focus in “Words and Graphs” by Kitaev and Lozin. A word w = w1 · · ·wn avoids the pattern 132 if there are no 1 ≤ i1 < i2 < i3 ≤ n such that wi1 < wi3 < wi2. A… (More)

- Alice L. L. Gao, Sergey Kitaev, Philip B. Zhang
- Discrete Applied Mathematics
- 2016

Abstract. A word w = w1w2 · · ·wn is alternating if either w1 < w2 > w3 < w4 > · · · (when the word is up-down) or w1 > w2 < w3 > w4 < · · · (when the word is down-up). In this paper, we initiate the study of (pattern-avoiding) alternating words. We enumerate up-down (equivalently, down-up) words via finding a bijection with order ideals of a certain poset.… (More)

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