Petar Marković - Publications

Books

2. P.Marković, Problem konačne baze identiteta u Univerzalnoj algebri, prvi deo. University of Novi Sad, 2015 (Serbian, cyrillic).

This monograph is an overview of the finite basis results which do not use commutator theory. It includes an introduction in basic Universal algebra and Model theory, so it is self-contained to a large extent.

1. P.Đapić, R.Sz.-Madarasz, P.Marković, Zbirka zadataka iz Univerzalne algebre, University of Novi Sad, 2014 (Serbian).

This is a problem book which accompanies an earlier Universal algebra textbook by the second author. It contains over 600 solved exercises ranging in difficulty from trivial to research-level. Primarily intended for students of master and PhD studies, it also contains some material which may be useful for researchers.

Journal Papers

On copyright: All papers are linked; on is the link to the pdf file. In the cases of journals with restricted access to content, the version linked is a near-final one, while in the cases of journals with fully open access, the version linked is the final one.

2018

22. N.Draganić, P.Marković, V.Uljarević, S.Zahirović, A characterization of idempotent strong Mal'cev conditions for congruence meet-semidistributivity in locally finite varieties. Algebra Universalis 79 (2018), article no. 53, 34pp.

21. P.Đapić, P.Marković, B.Martin, Quantified Constraint Satisfaction Problem on semicomplete digraphs. ACM Transactions on Computational Logic 18/1 (2017), article no. 2, 47pp.

2016

20. J.Jovanović, P.Marković, R.McKenzie, M.Moore, Optimal strong Mal'cev conditions for congruence meet-semidistributivity in locally finite varieties. Algebra Universalis 76 (2016), 305-325.

19. P.Đapić, P.Marković, Residual character of quasilinear varieties of groupoids. Publ. Inst. Math. (Beograd) 99(113) (2016), 15-30.

2015

18. M.S.Kurilić, P.Marković, Maximal antichains of isomorphic subgraphs of the Rado graph. Filomat 29 (2015), 1919-1923.

2014

17. K.A.Kearnes, P.Marković and R.McKenzie, Optimal strong Mal'cev conditions for omitting type 1 in locally finite varieties.
Algebra Universalis 72 (2014), 91-100.

2012

16. P.Marković, M.Maróti and R.McKenzie, Finitely related clones and algebras with cube terms. Order 29 (2012), 345-359.

2010

15. P.Đapić, J.Ježek, P.Marković, Star-quasilinear equational theories of groupoids. Studia Sci. Math. Hungar. 47 (2010), 267-288.

14. P.Idziak, P.Marković, R.McKenzie, M.Valeriote, R.Willard, Tractability and learnability arising from algebras with few subpowers. SIAM J. Comput. 39 (2010), 3023-3037.

13. J.Berman, P.Idziak, P.Marković, R.McKenzie, M.Valeriote, R.Willard, Varieties with few subalgebras of powers. Trans. Amer. Math. Soc. 362 (2010), 1445-1473.

2009

12. C.A.Carvalho, V.Dalmau, P.Marković, M.Maróti, CD(4) has bounded width. Algebra Universalis 60 (2009), 293-307.

2008

11. I.Bošnjak, P.Marković, The 11-element case of Frankl's conjecture, Electronic J. Comb. 15(1) (2008), R88.


10. P.Marković, R.McKenzie, Few subpowers, congruence distributivity and near-unanimity. Algebra Universalis 58 (2008), 119-128.

2007

9. P.Marković, An attempt at Frankl's conjecture. In: Proceedings of the 2nd Novi Sad Algebraic Conference (NSAC 2005), a special issue of Publ. Inst. Math. (Beograd) 81(95) (2007), 29-43.

8.J.Ježek, P.Marković, D.Stanovsky, Homomorphic images of finite subdirectly irreducible unary algebras. Czechoslovak Math. J. 57(132) (2007), 671-677.

7. P.Đapić, J.Ježek, P.Marković, R.McKenzie, D.Stanovsky, Star-linear equational theories of groupoids. Algebra Universalis 56 (2007), 357-397.

2004

6. I.Dolinka, P.Marković, The Berman conjecture is true for nilpotent extensions of regular semigroups. Algebra Universalis 51 (2004), 435-438.

2002

5. R.Freese, J.Ježek, P.Jipsen, P.Marković, M.Maróti, R.McKenzie, The variety generated by order algebras. Algebra Universalis 47 (2002), 103-138.

2000

4. J.Ježek, P.Marković, M.Maróti, R.McKenzie, Equations of tournaments are not finitely based. Discrete Math. 211 (2000), 243-248.

1999

3. J.Ježek, P.Marković, M.Maróti, R.McKenzie, The variety generated by tournaments. Acta Univ. Carolinae Math. Phys. 40 (1999), 21-41.

2. S.Crvenković, I.Dolinka, P.Marković, A survey of algebra of tournaments. In: Proceedings of the VIII International Conference “Algebra and Logic” (Novi Sad, 1998), a special issue of Novi Sad Journal of Mathematics 29 (2) (1999), 95-130.

1.  S.Crvenković, I.Dolinka, P.Marković, Decidability problems for the variety generated by tournaments. In: Proceedings of the VIII International Conference “Algebra and Logic” (Novi Sad, 1998), a special issue of Novi Sad Journal of Mathematics 29 (2) (1999), 85-93.

Conference Proceedings Papers

An explanation for mathematicians, who might find this category strange, like I did at first: Due to the custom in Computer Science to publish extended abstracts in conferences, I include such publications in this category. These extended abstracts are basically all results of a paper and all proofs which can fit in some small number of pages, usually a dozen or so. However, the referees also have access to the remaining proofs which are in the appendix (the appendix goes unpublished). Subsequently, it is customary to publish the same result in a journal version, which includes all proofs and also often is a better or updated version of the part which was already published. This is not considered self-plagiarism. Indeed, some conferences are very highly regarded and competitive to publish in, actually there are a number of conferences which a typical computer scientist will prefer to have published in than in any journal.

My papers which were published with all proofs written in the usual way are in the Journal Papers category, even if they were published in a journal which had a special issue devoted to the proceedings of a conference.

2. P.Đapić, P.Marković, B.Martin, QCSP on Semicomplete Digraphs.  In: Proceedings of the 41st International Colloquium on Automata, Languages and Programming - ICALP '14 (Copenhagen, Denmark, July 2014), vol. 1, pp. 847-858.

1. P.Idziak, P.Marković, R.McKenzie, M.Valeriote, R.Willard, Tractability and learnability arising from algebras with few subpowers. In: Proceedings of 22nd IEEE Symposium on Logic in Computer Science - LICS '07 (Wroclaw, Poland, July 2007), pp. 213-222.

Lectures

The following two recent lectures explain Vladimir Božin's approach to Frankl's Conjecture, a famous problem in Combinatorics. The Siena lecture gives a lot more information, but the Budapest lecture is easier to follow since some of the hard stuff is omitted. The Siena lecture is sufficient for an interested reader to reconstruct the whole proof of Božin's Equivalence Theorem, in my opinion.

2. V.Božin, P.Marković, An equivalent condition to Frankl's Conjecture. Combinatorics seminar (Budapest, Hungary, November 2020).

1. P.Marković, On Vladimir Božin's equivalent to Frankl's union-closed sets conjecture. Plenary talk at Arbeitstagung Allgemeine Algebra 99 (Siena, Italy, February 2020).