601
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Conditions for matchability in groups and field extensions

, , , &
Pages 1182-1197 | Received 23 Jul 2021, Accepted 11 Mar 2022, Published online: 31 Mar 2022

References

  • Fan CK, Losonczy J. Matchings and canonical forms for symmetric tensors. Adv Math. 1996;117(2):228–238.
  • Wakeford EK. On canonical forms. Proc London Math Soc (2). 1920;18:403–410.
  • Aliabadi M, Filom K. Results and questions on matchings in groups and vector subspaces of fields. J Algebra. 2022;598:85–104.
  • Alon N, Fan CK, Kleitman D, et al. Acyclic matchings. Adv Math. 1996;122(2):234–236.
  • Eliahou S, Lecouvey C. Matchings in arbitrary groups. Adv Appl Math. 2008;40(2):219–224.
  • Eliahou S, Lecouvey C. Matching subspaces in a field extension. J Algebra. 2010;324(12):3420–3430.
  • Aliabadi M. Matchings in groups and vector spaces [PhD thesis]. University of Illinois at Chicago; 2020. 103 pp.
  • Aliabadi M, Hadian M, Jafari A. On matching property for groups and field extensions. J Algebra Appl. 2016;15(1):Article ID 1650011, 13.
  • Aliabadi M, Janardhanan MV. On local matching property in groups and vector spaces. Australas J Combin. 2018;70:75–85.
  • Aliabadi M, Janardhanan MV. On matchable subsets in abelian groups and their linear analogues. Linear Algebra Appl. 2019;582:138–155.
  • Rado R. A theorem on independence relations. Quart J Math Oxford Ser. 1942;13:83–89.
  • Losonczy J. On matchings in groups. Adv Appl Math. 1998;20(3):385–391.
  • Hall P. On representatives of subsets. J London Math Soc. 1935;10(1):26–30.
  • Hamidoune YO. Counting certain pairings in arbitrary groups. Combin Probab Comput. 2011;20(6):855–865.
  • Friedland S, Aliabadi M. Linear algebra and matrices. Philadelphia (PA): SIAM; 2018.
  • Roman S. Advanced linear algebra. New York: Springer; 2008. (Graduate texts in mathematics).
  • Heden O. On partitions of finite vector spaces of small dimensions. Arch Math (Basel). 1984;43(6):507–509.
  • Javaheri M. Projective partitions of vector spaces. Electron J Linear Algebra. 2017;32:125–130.
  • Khare A. Vector spaces as unions of proper subspaces. Linear Algebra Appl. 2009;431(9):1681–1686.
  • Luh J. On the representation of vector spaces as a finite union of subspaces. Acta Math Acad Sci Hungar. 1972;23:341–342.
  • Bachoc C, Serra O, Zémor G. Revisiting Kneser's theorem for field extensions. Combinatorica. 2018;38(4):759–777.
  • Nathanson MB. Additive number theory: inverse problems and the geometry of sumsets. New York: Springer-Verlag; 1996. (Graduate texts in mathematics; vol. 165).
  • Brualdi RA, Friedland S, Pothen A. The sparse basis problem and multilinear algebra. SIAM J Matrix Anal Appl. 1995;16(1):1–20.
  • Friedland S, Li Q, Schonfeld D. Compressive sensing of sparse tensors. IEEE Trans Image Process. 2014;23(10):4438–4447.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.