Acta Mechanica Slovaca 2019, 23(2):6-19 | DOI: 10.21496/ams.2019.015

Shellability of Pointed Integer Partition

Samuel Asefa Fufa1, Ayichew Abebe Gebeyehu1
1 Department of Mathematics, Adiss Ababa University, Ethiopia Bonga Collages of Teachers Education

In this paper we study, pointed integer partition defined as a pair where is an integer partition of n - m, and m is a non-negative integer ≤ n. Shellability of pointed integer partition with Möbius values -1 and +1 denoted by . We determine the cardinality of and for 1 ≤ n ≤ 10 and n ≥ 1 respectively and compute the Möbius number of for 1 ≤ n ≤ 6. We have shown hat admit an EL-labeling which is EL-shellable.

Keywords: Pointed Integer Partition, Hassee Diagram, Möbius Values and EL-Shellability.

Published: June 28, 2019  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Fufa, S.A., & Abebe Gebeyehu, A. (2019). Shellability of Pointed Integer Partition. Acta Mechanica Slovaca, 23(2), 6-19. doi: 10.21496/ams.2019.015
Share...
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. A. Björner, Shellable and Cohen-Macaulay partially ordered sets, (1980), 159-183. Go to original source...
    2. R. Ehrenborg and M. Readdy, The Möbius function of partitions with restricted block sizes, 2007, 1-3
    3. Patricia Hersh, Lexicographic Shellability for Balanced Complexes, Department of Mathematics, University of Washington, Seattle, Revised March 4, 2002, 226-228
    4. Dmitry Kozlov, Combinatorial Algebraic Topology, 2007, 219-224 Go to original source...
    5. Toufik Mansor, Combinatorics of Set Partitions, 2013, 1-5
    6. Brüggemann.R.Patil, Introduction To partial Order Application, 2011, 19-21 Go to original source...
    7. S.A.Fufa, On the Möbius Function of Pointed Partitions and Exponential Pointed Structures, Doctoral dissertation, University of Addis Ababa, 2015, 37-39, 56-57
    8. S.A.Fufa; M.Zeleke, (2018): On Möbius Function of Pointed Graded Lattice. Indian J Pure Appl Math (2018) 49: 51. Go to original source...
    9. Jay Schweig and Russ Woodroofe, a Broad class of Shellable Lattices, 2016, 7-9 Press,Cambridge, 1999.
    10. R. P. Stanley, Enumerative Combinatorics I, Second Edition, Cambridge University Press, Cambridge, 2011, 277-280 Go to original source...

    This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content