L-Covering Sets and L-Covering Polynomials of Chains

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-48 Number-4
Year of Publication : 2017
Authors : K.M.Thirunavukkarasu, A.Vethamanickam
  10.14445/22315373/IJMTT-V48P535

MLA

K.M.Thirunavukkarasu, A.Vethamanickam "L-Covering Sets and L-Covering Polynomials of Chains", International Journal of Mathematics Trends and Technology (IJMTT). V48(4):237-239 August 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
Let P be a finite poset.Fora subset A ofP, the open lower cover set of A is defined as L(A)={x P|x is covered by an a A}.

Reference
[1] M. Bayer and J. Billera, Counting chains and Faces in Polytopes andPosets, Contemporary Mathematics, 34, 207-252 (1984).
[2] P. Crawley and R.P.Dilworth, Algebraic theory of Lattices, Prentice-Hall, Inc. Englewod, Cliffs, New Jersey. 1973.
[3] B.A Davey and H.A.Priestley, Introduction to Lattices and Order, Second Edition, Cambridge University Press, 2002.
[4] Garrett Birkhoff, Lattice Theory, American Mathematical Society Colloquim Publications, Vol.XXV, 1961.
[5] G.Grätzer, General Lattice Theory, BirkhauserVerlag, Basel, 1978.
[6] Greene C. On the Mobius algebra of a partially ordered set, Advances in math. 10, 177-187(1973).
[7] Gunter M. Ziegler, Lectures on Polytopes, Springer – Verlag, New York, Inc., 1995.
[8] Paffenholz and Andreas, Construction for posets, Lattices, and Polytopes, Doctoral Dissertation, School of Mathematical and Natural Sciences, Technical University of Berlin, 2005.
[9] SaeidAlikhani and Yee-Hock Peng, Dominating Sets and Domination Polynomials of Paths, International Journal of Mathematics and Mathematical Sciences, Vol.2009, PP.1-10.
[10] R.P.Stanley, Enumerative Combinatorics, Volume 1, Wordsworth and Brooks / Cole, 1986.
[11] R.Subbarayan andA.Vethamanickam, On the Lattice of Convex Sub lattices, Elixir Dis. Math. 50 (2012), 10471-10474.
[12] A.Vethamanickam, Topics in Universal Algebra, Ph.D. Thesis, Madurai Kamaraj University, 1994.
[13] A.Vethamanickam,and R.Subbarayan, Simple extensions of Eulerian Lattices, Acta Math. Univ. Comenianae, Vol. LXXIX, I(2010), PP.47-54.
[14] A.Vethamanickam and R.Subbarayan, Some Properties of Eulerian Lattices, CommentationesMathematicaeUniversitatitsCarolinae, Vol.55 (2014), (4) PP.499-507.
[15] A.Vethamanickam and K.M.Thirunavukkarasu, U-covering sets and U-covering polynomials of chains, International Journal of Mathematical Archive, Vol.8 (8), 2017, 41-44.

Keywords
Poset, L-Covering set, L-Covering Polynomial.