L-Covering Sets and L-Covering Polynomials
of Chains

K.M. Thirunavukkarasu; A. Vethamanickam

doi:https://doi.org/10.14445/22315373/IJMTT-V48P535

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 48 | Number 4 | Year 2017 | Article Id. IJMTT-V48P535 | DOI : https://doi.org/10.14445/22315373/IJMTT-V48P535

L-Covering Sets and L-Covering Polynomials of Chains

K.M. Thirunavukkarasu, A. Vethamanickam

Abstract

Let P be a finite poset.Fora subset A ofP, the open lower cover set of A is defined as L(A)={xP|x is covered by an aA}. The closed lower coverset of A is defined as L[A]=L(A) ∪ A and A is called an L – covering set of P if L[A] = P. The L – covering number ⋀(P) is the minimum cardinality of aL-covering set. Let 𝐿𝑛 𝑖 be the family of all L-covering sets of a chain Pn with cardinality i. Similarly we can define U–covering and N-covering sets of Pn with cardinality i. ℓ(Pn,i) = |𝐿𝑛 𝑖 |, 𝓊(Pn,i) = |𝑈𝑛 𝑖 |, 𝓃(Pn,i) = |𝑁𝑛 𝑖 |. In this paper, we construct 𝐿𝑛 𝑖 , and obtain a recursive formula for ℓ(Pn,i). Using this recursive formula we construct the polynomial L(Pn,x) = ℓ 𝑛 𝑖=0 𝑛 2 (Pn,i)xi called L-covering polynomial of Pn .

Keywords

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

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Citation :

K.M. Thirunavukkarasu, A. Vethamanickam, "L-Covering Sets and L-Covering Polynomials of Chains," International Journal of Mathematics Trends and Technology (IJMTT), vol. 48, no. 4, pp. 237-239, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V48P535