Full Paper View Go Back

The Mersenne Meet Matrices on A –Sets

N. Elumalai1 , R. Kalpana2

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.4 , pp.371-373, Aug-2018


CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i4.371373


Online published on Aug 31, 2018


Copyright © N. Elumalai, R. Kalpana . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library


XML View     PDF Download

How to Cite this Paper

  • IEEE Citation
  • MLA Citation
  • APA Citation
  • BibTex Citation
  • RIS Citation

IEEE Style Citation: N. Elumalai, R. Kalpana, “The Mersenne Meet Matrices on A –Sets,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.5, Issue.4, pp.371-373, 2018.

MLA Style Citation: N. Elumalai, R. Kalpana "The Mersenne Meet Matrices on A –Sets." International Journal of Scientific Research in Mathematical and Statistical Sciences 5.4 (2018): 371-373.

APA Style Citation: N. Elumalai, R. Kalpana, (2018). The Mersenne Meet Matrices on A –Sets. International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(4), 371-373.

BibTex Style Citation:
@article{Elumalai_2018,
author = {N. Elumalai, R. Kalpana},
title = {The Mersenne Meet Matrices on A –Sets},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {8 2018},
volume = {5},
Issue = {4},
month = {8},
year = {2018},
issn = {2347-2693},
pages = {371-373},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=750},
doi = {https://doi.org/10.26438/ijcse/v5i4.371373}
publisher = {IJCSE, Indore, INDIA},
}

RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v5i4.371373}
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=750
TI - The Mersenne Meet Matrices on A –Sets
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - N. Elumalai, R. Kalpana
PY - 2018
DA - 2018/08/31
PB - IJCSE, Indore, INDIA
SP - 371-373
IS - 4
VL - 5
SN - 2347-2693
ER -

410 Views    185 Downloads    131 Downloads
  
  

Abstract :
A recursive structure theorem for Mersenne meet matrices on A-sets is verified and a recursive formula for det (Mersenne meet matrix) and for inverse of (Mersenne meet matrix) on A-sets is also verified. The recursive formulae also yield explicit formulae, e.g. the known determinant and inverse formulae on chains and a-sets.

Key-Words / Index Term :
Meet Matrices, Mersenne Meet Matrices, a- Set, A-Set

References :
[1] P. Haukkanen, “On meet matrices on posets”, Linear
Algebra Appl. 249: 111-123 ,1996.
[2] B. V. Rajarama Bhat, “On greatest common divisor
matrices and their applications”, Linear Algebra Appl.
158: 77-97 ,1991.
[3] B. Wang, “Explicit Expressions of Smith`s Determinant
on a Poset”, Acta Math Sin.(Engl. Ser.), 17(1): 161-168,
2001.
[4] I. Korkee and P. Haukkanen, “Bounds for determinants of
meet matrices associated with incidence functions”,
Linear Algebra Appl. 329(1-3): 77-88 ,2001.
[5] I. Korkee and P. Haukkanen, “On meet matrices with
respect to reduced, extended and exchanged sets”, JP J.
Algebra Number Theory Appl., 4(3),559-575 ,2004.
[6] I. Korkee, “On meet and join matrices on A-sets and
Related Sets”, Notes on Number theory and Discrete
Mathematics, 10(3):57-67,2004.
[7] S. Beslin and S. Ligh, “GCD-closed sets and the
determinants of GCD matrices”, Fibonacci Quart.,
30: 157-160 ,1992.
[8] P. Haukkanen, J.Wang and J. SillanpÄaÄa, “On Smith`s
Determinant”, Linear Algebra Appl 258: 251-269 , 1997.
[9] [P. Haukkanen and J. SillanpÄaÄa, “Some analogues of
Smith`s determinant”, Linear an Multilinear Algebra
41: 233-244 ,1996.
[10] I. Korkee and P. Haukkanen, “On meet and join matrices
associated with incidence functions”.Linear Algebra
Appl., 372: 127-153 , 2003.
[11] M. Aigner, “Combinatorial Theory”. Springer-Verlag,
1979.
[12] G. Birkhof, “Lattice Theory”. American Mathematical
Society Colloquium Publication, 25,Rhode Island, 1984.
[13] R. A. Horn, C. R. Johnson, “Matrix Analysis”, Cambridge
University Press, New York ,1985.
[14] I. Korkee, “ A note on meet and join matrices and their
special cases GCUD and LCUM Matrices”, Int. J. Pure
Appl. Math.1-11
[15] F. Zhang, “Matrix theory”. Basic results and techniques,
Universitext, Springer-Verlag, New York, 1999.
[16] Parthajit Roy, Swati Adhikari and J. K. Mandal, “A
Shortest Path Similarity Matrix based Spectral
Clustering”, International Journal of Computer
Sciences and Engineering 4(1) , 2015.

Authorization Required

 

You do not have rights to view the full text article.
Please contact administration for subscription to Journal or individual article.
Mail us at  support@isroset.org or view contact page for more details.

Go to Navigation