Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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DISCRETE VOLUME OF THE POSET POLYTOPE FOR A VARIANT OF UP-DOWN POSETS

  • Byeong-Gil Choe (Department of Mathematics Chonnam National University) ;
  • Hyeong-Kwan Ju (Department of Mathematics Chonnam National University) ;
  • Kyu-Chul Shim (Department of Mathematics Chonnam National University)
  • Received : 2023.10.23
  • Accepted : 2023.11.21
  • Published : 2023.11.30
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Abstract

Discrete volumes of poset polytopes for a variant of up-down posets introduced in [4] were studied. We obtained the generating functions for the discrete volumes of poset polytopes for a variant of up-down poset using the characteristic matrices.

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References

  1. M. Beck and S. Robins, Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra, UTM (2nd ed.), Springer, New York, 2007.
  2. The Online Encylopedia of Integer Sequences(OEIS) http://oeis.org.
  3. H.-K. Ju, On the Sequence Generated by a Certain Type of Matrices, Honam Math. J., 39(2017), 665-675.
  4. H.-K. Ju and K.-C. Shim, Number of Linear Extension for a Variant of Up-down Posets, Honam Math. J., 43(2021), 741-749.
  5. G. Xin and Y. Zhong, Proving Some Conjectures on Kekul'e Numbers for Certain Benzenoids by Using Chebyshev Polynomials, Adv. in Applied Math., 415(2023), and also available at https://doi.org/10.1016/j.aam.2022.102479.