Mathematica Pannonica
Volume/Issue:
Volume 28_NS2: Issue 1
Proof of a Conjecture of Proctor and Scoppetta Related to d-Complete Posets
Author:
Jonathan David Farley Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, United States of America

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Pages:
69–75
Online Publication Date:
09 Mar 2022
Publication Date:
26 Apr 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/314.2022.00009
Keywords:
(Partially) ordered set; d-complete poset
Open access

Proctor and Scoppetta conjectured that

  • (1) there exists an infinite locally finite poset that satisfies their conditions VT and NTC but not SIS;

  • (2) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MF but not both VT and FT; and

  • (3) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MD but not NCC.

In this note, the conjecture of Proctor and Scoppetta, which is related to d-complete posets, is proven.

  • [1]

    Birkhoff, G. Lattice Theory (third edition). American Mathematical Society, Providence, Rhode Island, 1967.

  • [2]

    Davey, B. A., and Priestley, H. A. Introduction to Lattices and Order (second edition). Cambridge University Press, Cambridge, 2002.

  • [3]

    Farley, J. D. Cancel Culture: The Search for Universally Cancellable Exponents ofPosets. Manuscript (2021).

  • [4]

    Proctor, R. A., and Scoppetta, L. M. d-complete Posets: Local Structural Axioms, Properties, and Equivalent Definitions. Order 36 (2019), 399-422.

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Mathematica Pannonica
Print ISSN:
0865-2090
Online ISSN:
2786-0752

Editor in Chief: László TÓTH, University of Pécs, Pécs, Hungary

Honorary Editors in Chief:

  • János PINTZ, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • † Ferenc SCHIPP, Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary
  • Sándor SZABÓ, University of Pécs, Pécs, Hungary
     

Deputy Editors in Chief:

  • Erhard AICHINGER, JKU Linz, Linz, Austria
  • Ferenc HARTUNG, University of Pannonia, Veszprém, Hungary
  • Ferenc WEISZ, Eötvös Loránd University, Budapest, Hungary

Editorial Board

  • Attila BÉRCZES, University of Debrecen, Debrecen, Hungary
  • István BERKES, Rényi Institute of Mathematics, Budapest, Hungary
  • Károly BEZDEK, University of Calgary, Calgary, Canada
  • György DÓSA, University of Pannonia, Veszprém, Hungary
  • Balázs KIRÁLY – Managing Editor, University of Pécs, Pécs, Hungary
  • Vedran KRCADINAC, University of Zagreb, Zagreb, Croatia 
  • Željka MILIN ŠIPUŠ, University of Zagreb, Zagreb, Croatia
  • Gábor NYUL, University of Debrecen, Debrecen, Hungary
  • Margit PAP, University of Pécs, Pécs, Hungary
  • István PINK, University of Debrecen, Debrecen, Hungary
  • Mihály PITUK, University of Pannonia, Veszprém, Hungary
  • Lukas SPIEGELHOFER, Montanuniversität Leoben, Leoben, Austria
  • Andrea ŠVOB, University of Rijeka, Rijeka, Croatia
  • Csaba SZÁNTÓ, Babeş-Bolyai University, Cluj-Napoca, Romania
  • Jörg THUSWALDNER, Montanuniversität Leoben, Leoben, Austria
  • Zsolt TUZA, University of Pannonia, Veszprém, Hungary

Advisory Board

  • Szilárd RÉVÉSZ – Chair, HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
  • Gabriella BÖHM
  • György GÁT, University of Debrecen, Debrecen, Hungary

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Mathematica Pannonica
Language English
Size A4
Year of
Foundation		 1990
Volumes
per Year		 1
Issues
per Year		 2
Founder Akadémiai Kiadó
Founder's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
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ISSN 2786-0752 (Online)
ISSN 0865-2090 (Print)

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