Finite partially ordered set and some of its properties

Authors

  • RN Yadav Department of Mathematics, M. M. A. M. Campus, Tribhuvan University, Biratnagar
  • SK Chakrabarti Department of Physics, M. M. A. M. Campus, Tribhuvan University, Biratnagar
  • IS Jha Department of Physics, M. M. A. M. Campus, Tribhuvan University, Biratnagar
  • UP Yadav Department of Mathematics, M. M. A. M. Campus, Tribhuvan University, Biratnagar

DOI:

https://doi.org/10.3126/bibechana.v13i0.13985

Keywords:

Poset, ferrers shape, duality theorem, functionality, recursive computation.

Abstract

This paper focuses on some main properties of the finite partially ordered sets. These properties are furnished in the form of theorems. Here we have presented three such theorems. The first theorem is called as ‘duality theorem’. This fundamental theorem was first obtained by Greene. Few years later it was rediscovered and given an alternative proof by Fomin. The second theorem bestows the functionality property. The proof of this was also done by Greene. However, Gansner gave an alternative proof of the theorem taking advantage of a connection between poset and linear algebra. The proof of the third theorem is fully due to us. This theorem gives rise to a recursive computation of the shape. In the present paper we have discussed the first two properties through suitable illustrations only whereas a complete proof is furnished for the last one.   

BIBECHANA 13 (2016) 126-130

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Published

2015-12-03

How to Cite

Yadav, R., Chakrabarti, S., Jha, I., & Yadav, U. (2015). Finite partially ordered set and some of its properties. BIBECHANA, 13, 132–136. https://doi.org/10.3126/bibechana.v13i0.13985

Issue

Section

Research Article