Erkko Lehtonen

Publications

Papers in refereed international scientific journals

  1. P. Jipsen, E. Lehtonen, R. Pöschel, \(S\)-preclones and the Galois connection \({}^S\mathrm{Pol}\)–\({}^S\mathrm{Inv}\), Part I, Algebra Universalis 85 (2024) Art. 34, 29 pp. [DOI] [SharedIt]
  2. M. Couceiro, E. Lehtonen, Stability of Boolean function classes with respect to clones of linear functions, Order 41 (2024) 15–64. [DOI] [SharedIt]
  3. M. Couceiro, E. Lehtonen, Galois theory for analogical classifiers, Ann. Math. Artif. Intell. 92 (2024) 29–47. [DOI]
  4. E. Lehtonen, Majority-closed minions of Boolean functions, Algebra Universalis 85 (2024) Art. 6, 48 pp. [DOI] [SharedIt]
  5. E. Lehtonen, Permutations avoiding the complement of a regular permutation group, Discrete Math. Lett. 12 (2023) 150–153. [DOI]
  6. J. Huang, E. Lehtonen, The associative-commutative spectrum of a binary operation, Discrete Math. 346(10) (2023) Art. 113535, 22 pp. [DOI]
  7. E. Lehtonen, T. Waldhauser, Associative spectra of graph algebras II. Satisfaction of bracketing identities, spectrum dichotomy, J. Algebraic Combin. 55 (2022) 533–557. [DOI]
  8. A. J. Cain, E. Lehtonen, Reconstructing Young tableaux, J. Combin. Theory Ser. A 187 (2022) Art. 105578, 9 pp. [DOI]
  9. B. Bodor, E. Lehtonen, T. Quinn-Gregson, N. Verhulst, HS-stability and complex products in involution semigroups, Semigroup Forum 103 (2021) 395–413. [DOI]
  10. M. J. Gouveia, E. Lehtonen, Permutation reconstruction from a few large patterns, Electron. J. Combin. 28(3) (2021) #P3.41. [DOI]
  11. E. Lehtonen, T. Waldhauser, Associative spectra of graph algebras I. Foundations, undirected graphs, antiassociative graphs, J. Algebraic Combin. 53 (2021) 613–638. [DOI]
  12. E. Lehtonen, R. Pöschel, Reflections and powers of multisorted minions, Algebra Universalis, 82 (2021) Art. 20, 20 pp. [DOI]
  13. E. Lehtonen, C. Manyuen, Graph varieties axiomatized by semimedial, medial, and some other groupoid identities, Discuss. Math. Gen. Algebra Appl. 40 (2020) 143–157. [DOI]
  14. E. Lehtonen, N. Lekkoksung, Variants of essential arity for partial functions, Kyungpook Math. J. 60 (2020) 423–443. [DOI]
  15. E. Lehtonen, Permutation groups arising from pattern involvement, J. Algebraic Combin. 52 (2020) 251–298. [DOI] [SharedIt]
  16. E. Lehtonen, F. Starke, On associative operations on commutative integral domains, Semigroup Forum 100 (2020) 910–915. [DOI] [SharedIt]
  17. E. Lehtonen, R. Pöschel, Graph quasivarieties, Acta Sci. Math. (Szeged) 86 (2020) 31–50. [DOI]
  18. M. Couceiro, E. Lehtonen, P. Mercuriali, R. Péchoux, On the efficiency of normal form systems for representing Boolean functions, Theoret. Comput. Sci. 813 (2020) 341–361. [DOI]
  19. E. Lehtonen, Content and singletons bring unique identification minors, J. Aust. Math. Soc. 107 (2019) 67–90. [DOI]
  20. E. Lehtonen, T. Waldhauser, Minor posets of functions as quotients of partition lattices, Order 36 (2019) 23–41. [DOI] [SharedIt]
  21. E. Lehtonen, R. Pöschel, T. Waldhauser, Reflections on and of minor-closed classes of multisorted operations, Algebra Universalis 79 (2018) Art. 71, 19 pp. [DOI] [SharedIt]
  22. E. Lehtonen, R. Pöschel, T. Waldhauser, Reflection-closed varieties of multisorted algebras and minor identities, Algebra Universalis 79 (2018) Art. 70, 22 pp. [DOI] [SharedIt]
  23. M. Couceiro, E. Lehtonen, Majors of functions, Order 35 (2018) 233–246. [DOI] [SharedIt]
  24. E. Lehtonen, R. Pöschel, Permutation groups, pattern involvement, and Galois connections, Acta Sci. Math. (Szeged) 83 (2017) 355–375. [DOI]
  25. M. Couceiro, E. Lehtonen, On the arity gap of finite functions: results and applications, J. Mult.-Valued Logic Soft Comput. 27 (2016) 193–207. [link]
  26. E. Lehtonen, On functions with a unique identification minor, Order 33 (2016) 71–80. [DOI]
  27. E. Lehtonen, Reconstructing permutations from identification minors, Electron. J. Combin. 22(4) (2015) #P4.20. [DOI]
  28. E. Lehtonen, A. Pilitowska, Entropicity and generalized entropic property in idempotent n-semigroups, Semigroup Forum 91 (2015) 260–281. [DOI]
  29. M. Couceiro, E. Lehtonen, K. Schölzel, Hypomorphic Sperner systems and non-reconstructible functions, Order 32 (2015) 255–292. [DOI]
  30. M. Couceiro, E. Lehtonen, K. Schölzel, Set-reconstructibility of Post classes, Discrete Appl. Math. 187 (2015) 12–18. [DOI]
  31. M. Couceiro, E. Lehtonen, K. Schölzel, A complete classification of equational classes of threshold functions included in clones, RAIRO Oper. Res. 49 (2015) 39–66. [DOI]
  32. M. Couceiro, E. Lehtonen, T. Waldhauser, A survey on the arity gap, J. Mult.-Valued Logic Soft Comput. 24 (2015) 223–249. [link]
  33. M. Couceiro, E. Lehtonen, T. Waldhauser, On equational definability of function classes, J. Mult.-Valued Logic Soft Comput. 24 (2015) 203–222. [link]
  34. E. Lehtonen, J.-L. Marichal, B. Teheux, Associative string functions, Asian-Eur. J. Math. 7(4) (2014) 1450059, 18 pp. [DOI]
  35. M. Couceiro, E. Lehtonen, T. Waldhauser, Additive decomposition schemes for polynomial functions over fields, Novi Sad J. Math. 44(2) (2014) 89–105. [index] [PDF]
  36. E. Lehtonen, A. Pilitowska, Generalized entropy in expanded semigroups and in algebras with neutral element, Semigroup Forum 88 (2014) 702–714. [DOI]
  37. E. Lehtonen, Totally symmetric functions are reconstructible from identification minors, Electron. J. Combin. 21(2) (2014) #P2.6. [DOI]
  38. E. Lehtonen, Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings, Internat. J. Algebra Comput. 24 (2014) 11–31. [DOI]
  39. M. Couceiro, E. Lehtonen, T. Waldhauser, Parametrized arity gap, Order 30 (2013) 557–572. [DOI]
  40. M. Couceiro, E. Lehtonen, T. Waldhauser, Additive decomposability of functions over abelian groups, Internat. J. Algebra Comput. 23 (2013) 643–662. [DOI]
  41. M. Behrisch, M. Couceiro, K. A. Kearnes, E. Lehtonen, Á. Szendrei, Commuting polynomial operations of distributive lattices, Order 29 (2012) 245–269. [DOI]
  42. M. Couceiro, E. Lehtonen, Galois theory for sets of operations closed under permutation, cylindrification, and composition, Algebra Universalis 67 (2012) 273–297. [DOI]
  43. M. Couceiro, E. Lehtonen, T. Waldhauser, The arity gap of order-preserving functions and extensions of pseudo-Boolean functions, Discrete Appl. Math. 160 (2012) 383–390. [DOI]
  44. M. Couceiro, E. Lehtonen, T. Waldhauser, Decompositions of functions based on arity gap, Discrete Math. 312 (2012) 238–247. [DOI]
  45. L. Kwuida, E. Lehtonen, On the homomorphism order of labeled posets, Order 28 (2011) 251–265. [DOI]
  46. M. Couceiro, E. Lehtonen, Self-commuting lattice polynomial functions on chains, Aequationes Math. 81 (2011) 263–278. [DOI]
  47. E. Lehtonen, Á. Szendrei, Clones with finitely many relative R-classes, Algebra Universalis 65 (2011) 109–159. [DOI]
  48. E. Lehtonen, A note on minors determined by clones of semilattices, Novi Sad J. Math. 40(3) (2010) 75–81. [index] [PDF]
  49. S. Foldes, E. Lehtonen, Column-partitioned matrices over rings without invertible transversal submatrices, Ars Combin. 97 (2010) 33–39. [index]
  50. E. Lehtonen, Closed classes of functions, generalized constraints, and clusters, Algebra Universalis 63 (2010) 203–234. [DOI]
  51. E. Lehtonen, Characterization of preclones by matrix collections, Asian-Eur. J. Math. 3 (2010) 457–473. [DOI]
  52. E. Lehtonen, Á. Szendrei, The submaximal clones on the three-element set with finitely many relative R-classes, Discuss. Math. Gen. Algebra Appl. 30 (2010) 7–33. [index] [PDF]
  53. E. Lehtonen, J. Nešetřil, Minors of Boolean functions with respect to clique functions and hypergraph homomorphisms, European J. Combin. 31 (2010) 1981–1995. [DOI]
  54. M. Couceiro, E. Lehtonen, Generalizations of Świerczkowski’s lemma and the arity gap of finite functions, Discrete Math. 309 (2009) 5905–5912. [DOI]
  55. E. Lehtonen, Á. Szendrei, Equivalence of operations with respect to discriminator clones, Discrete Math. 309 (2009) 673–685. [DOI]
  56. E. Lehtonen, Labeled posets are universal, European J. Combin. 29 (2008) 493–506. [DOI]
  57. M. Couceiro, E. Lehtonen, On the effect of variable identification on the essential arity of functions on finite sets, Int. J. Found. Comput. Sci. 18 (2007) 975–986. [DOI]
  58. M. Couceiro, S. Foldes, E. Lehtonen, Composition of Post classes and normal forms of Boolean functions, Discrete Math. 306 (2006) 3223–3243. [DOI]
  59. E. Lehtonen, Descending chains and antichains of the unary, linear, and monotone subfunction relations, Order 23 (2006) 129–142. [DOI]

Papers in proceedings of international conferences

  1. J. Huang, E. Lehtonen, The associative-commutative spectrum of a binary operation, Proceedings of the 35th Conference on Formal Power Series and Algebraic Combinatorics (Davis), Sém. Lothar. Comb. 89B (2023) Art. #10, 12 pp. [link]
  2. M. Couceiro, E. Lehtonen, A Galois framework for the study of analogical classifiers, in: M. Couceiro, P.-A. Murena (eds.), IJCAI-ECAI Workshop on the Interactions between Analogical Reasoning and Machine Learning (IARML@IJCAI-ECAI 2022), 23–25 July 2022, Vienna, Austria, pp. 55–65, HAL Id: hal-03745365. [link]
  3. M. Couceiro, E. Lehtonen, L. Miclet, H. Prade, G. Richard, When nominal analogical proportions do not fail, in: J. Davis, K. Tabia (eds.), Scalable Uncertainty Management, SUM 2020, Lecture Notes in Computer Science 12322, Springer, Cham, 2020, pp. 68–83, ISBN: 978-3-030-58448-1, 978-3-030-58449-8. [DOI]
  4. M. Couceiro, E. Lehtonen, Linearly definable classes of Boolean functions, in: M. Couceiro, P. Monnin, A. Napoli (eds.), Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020), Université de Lorraine, Nancy, 2020, pp. 39–46, HAL Id: hal-02918958. [link] Also appeared in: M. Couceiro, P. Monnin, A. Napoli (eds.), Proceedings of the First International Conference “Algebras, graphs and ordered sets” (ALGOS 2020), CEUR Workshop Proceedings, Vol. 2925, CEUR-WS.org, 2021, pp. 21–28, ISSN: 1613-0073. [contents] [PDF]
  5. E. Lehtonen, T. Waldhauser, Posets of minors of functions in multiple-valued logic, 2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL 2017), IEEE Computer Society, Los Alamitos, 2017, pp. 43–48, ISBN: 978-1-5090-5495-4. [DOI]
  6. M. Couceiro, E. Lehtonen, K. Schölzel, Sur des classes de fonctions à seuil caractérisables par des contraintes relationnelles — On classes of threshold functions characterizable by relational constraints, in: J.-L. Marichal, N. Essounbouli, K. Guelton (eds.), Actes des 22èmes rencontres francophones sur la Logique Floue et ses Applications (LFA 2013), Université de Reims Champagne-Ardenne, 2013, pp. 145–152. [PDF]
  7. M. Couceiro, E. Lehtonen, T. Waldhauser, Gap vs. pag, 42nd IEEE International Symposium on Multiple-Valued Logic (ISMVL 2012), IEEE Computer Society, Los Alamitos, 2012, pp. 268–273, ISBN: 978-0-7695-4673-5. [DOI]
  8. E. Lehtonen, Á. Szendrei, Partial orders induced by quasilinear clones, Contributions to General Algebra 20, Proceedings of the Salzburg Conference 2011 (AAA81), Verlag Johannes Heyn, Klagenfurt, 2012, pp. 51–84, ISBN: 978-3-7084-0447-9. [preprint]
  9. M. Couceiro, E. Lehtonen, J.-L. Marichal, T. Waldhauser, An algorithm for producing median formulas for Boolean functions, Proceedings of the Reed–Muller 2011 Workshop, Tampere International Center for Signal Processing (TICSP), 2011, pp. 49–54.
  10. M. Couceiro, E. Lehtonen, T. Waldhauser, A survey on the arity gap, 41st IEEE International Symposium on Multiple-Valued Logic (ISMVL 2011), IEEE Computer Society, Los Alamitos, 2011, pp. 277–281, ISBN: 978-0-7695-4405-2. [DOI]
  11. M. Couceiro, E. Lehtonen, T. Waldhauser, On equational definability of function classes, 41st IEEE International Symposium on Multiple-Valued Logic (ISMVL 2011), IEEE Computer Society, Los Alamitos, 2011, pp. 182–186, ISBN: 978-0-7695-4405-2. [DOI]
  12. M. Couceiro, E. Lehtonen, T. Waldhauser, On the arity gap of aggregation functions, in: D. Dubois, M. Grabisch, R. Mesiar, E. P. Klement (eds.), 32nd Linz Seminar on Fuzzy Set Theory (LINZ 2011) — Decision Theory: Qualitative and Quantitative Approaches, Johannes Kepler Universität, Linz, 2011, pp. 25–28.
  13. M. Couceiro, E. Lehtonen, Explicit descriptions of bisymmetric Sugeno integrals, in: E. Hüllermeier, R. Kruse, F. Hoffmann (eds.), Computational Intelligence for Knowledge-Based Systems Design, Lecture Notes in Artificial Intelligence 6178, Springer-Verlag, Berlin, Heidelberg, 2010, pp. 494–501, ISBN: 978-3-642-14048-8. [DOI]
  14. M. Couceiro, E. Lehtonen, Classes of operations closed under permutation, cylindrification and composition, 40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010), IEEE Computer Society, Los Alamitos, 2010, pp. 117–121, ISBN: 978-0-7695-4024-5. [DOI]
  15. M. Couceiro, E. Lehtonen, The arity gap of polynomial functions over bounded distributive lattices, 40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010), IEEE Computer Society, Los Alamitos, 2010, pp. 113–116, ISBN: 978-0-7695-4024-5. [DOI]
  16. M. Couceiro, E. Lehtonen, On the arity gap of finite functions: results and applications, in: Y. Boudabbous, N. Zaguia (eds.), Proceedings of the First International Conference on Relations, Orders and Graphs: Interaction with Computer Science (ROGICS ’08), Nouha Editions, Sfax, 2008, pp. 65–72, ISBN: 978-0-9809498-0-3.
  17. E. Lehtonen, An infinite descending chain of Boolean subfunctions consisting of threshold functions, Contributions to General Algebra 17, Proceedings of the Vienna Conference 2005 (AAA70), Verlag Johannes Heyn, Klagenfurt, 2006, pp. 145–148, ISBN: 3-7084-0194-8.
  18. M. Couceiro, S. Foldes, E. Lehtonen, On the complexity of representing sets of vertices in the n-cube, in: C. Tsitouras, T. E. Simos, G. Psihoyios (eds.), ICNAAM 2005, Wiley-VCH, Weinheim, 2005, pp. 876–877, ISBN: 3-527-40652-2.
  19. M. Couceiro, S. Foldes, E. Lehtonen, On compositions of clones of Boolean functions, in: T. Simos, G. Maroulis (eds.), International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004), VSP/Brill, Utrecht, 2004, pp. 849–851, ISBN: 90-6764-418-8.

Theses

  1. E. Lehtonen, Reconstruction of functions from minors, habilitation thesis, Technische Universität Dresden, Dresden, 2018. [link]
  2. E. Lehtonen, Operations on finite sets, functional composition, and ordered sets, doctoral dissertation, Tampere University of Technology, Publication 680, Tampere, 2007, ISBN: 978-952-15-1849-2. [link]
  3. E. Lehtonen, End-to-end data security solutions with GPRS, master’s thesis, Tampere University of Technology, Tampere, 1998.

Research reports

  1. E. Lehtonen, J. Nešetřil, Minors of Boolean functions with respect to clique functions and hypergraph homomorphisms, ITI Series 2008-411, KAM-DIMATIA Series 2008-890, Charles University, 2008. [link] [link]
  2. S. Foldes, E. Lehtonen, A row-reduced form for column-partitioned matrices, RUTCOR Research Report RRR 8-2006, Rutgers University, 2006. [link] [PS]
  3. M. Couceiro, S. Foldes, E. Lehtonen, Composition of Post classes and normal forms of Boolean functions, RUTCOR Research Report RRR 5-2005, Rutgers University, 2005. [link] [PS]