호남수학학술지 (Honam Mathematical Journal)

  • 제41권4호
  • /
  • Pages.863-870
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  • 2019
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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LINEAR EXTENSIONS OF DIAMOND POSETS

  • Ju, Hyeong-Kwan (Department of Mathematics, Chonnam National University) ;
  • Seo, Seunghyun (Department of Mathematics Education, Kangwon National University)
  • 투고 : 2019.11.25
  • 심사 : 2019.12.03
  • 발행 : 2019.12.25
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초록

In this paper, we obtain the enumeration results on the number of linear extensions of diamond posets. We find the recurrence relations and exponential generating functions for the number of linear extensions of diamond posets. We also get some results for the volume of graph polytope associated with bipartite graphs which are underlying graphs of diamond posets.

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참고문헌

  1. Richard Beals and Roderick Wong, Special Functions, Cambridge studies in advanced mathematics 126, Cambridge University Press, 2010.
  2. Hyeong-Kwan Ju, Sangwook Kim and Daeseok Lee, Different volume computational methods of graph polytopes, Bull. Korean Math. Soc., 55(5) (2018), 1405-1417. https://doi.org/10.4134/BKMS.b170821
  3. Hyeong-Kwan Ju and Soo-Jeong Seo, Volume of graph polytopes for the path-star type graphs, Honam Math. J., 38(1) (2016), 71-84. https://doi.org/10.5831/HMJ.2016.38.1.71
  4. The Online Encyclopedia of Integer Sequences(OEIS), http://oeis.org.
  5. Richard P. Stanley, Enumerative Combinatorics, vol.1, Cambridge University Press, 2011.
  6. Grzegorz Stachowiak, The number of linear extensions of bipartite graphs, Order, 5 (1988), 257-259. https://doi.org/10.1007/BF00354893