Papers in International Journals

• Gouveia, M. J.; Lehtonen, Erkko (2021)  Permutation reconstruction from a few large patterns . Electronic Journal of Combinatorics: 28(3), #P3.41.

• Lehtonen, Erkko; Waldhauser, Tamás (2021)  Associative spectra of graph algebras I. Foundations, undirected graphs, antiassociative graphs . Journal of Algebraic Combinatorics: 53, 613–638.

• Bodor, Bertalan; Lehtonen, Erkko; Quinn-Gregson, Thomas; Verhulst, Nikolaas (2021)  HS-stability and complex products in involution semigroups . Semigroup Forum: 103, 395–413.

• Lehtonen, Erkko; Pöschel, Reinhard (2021)  Reflections and powers of multisorted minions . Algebra Universalis: 82, Art. 20.

• Lehtonen, Erkko; Lekkoksung, Nareupanat (2020)  Variants of essential arity for partial functions . Kyungpook Mathematical Journal: 60, 423–443.

• Lehtonen, Erkko; Starke, Florian (2020)  On associative operations on commutative integral domains . Semigroup Forum: 100, 910–915.

• Couceiro, Miguel; Lehtonen, Erkko; Mercuriali, Pierre; Péchoux, Romain (2020)  On the efficiency of normal form systems for representing Boolean functions . Theoretical Computer Science: 813, 341–361.

• Lehtonen, Erkko; Manyuen, Chaowat (2020)  Graph varieties axiomatized by semimedial, medial, and some other groupoid identities . Discussiones Mathematicae – General Algebra and Applications: 40, 143–157.

• Lehtonen, Erkko (2020)  Permutation groups arising from pattern involvement . Journal of Algebraic Combinatorics: 52, 251–298.

• Lehtonen, Erkko; Pöschel, Reinhard (2020)  Graph quasivarieties . Acta Sci. Math. (Szeged): 86, 31–50.

• Lehtonen, Erkko (2019)  Content and singletons bring unique identification minors . Journal of the Australian Mathematical Society: 107, 67–90.

• Lehtonen, Erkko; Waldhauser, Tamás (2019)  Minor posets of functions as quotients of partition lattices . Order: 36, 23–41.

• Lehtonen, Erkko; Pöschel, Reinhard; Waldhauser, Tamás (2018)  Reflection-closed varieties of multisorted algebras and minor identities . Algebra Universalis: 79, Art. 70, 22 pp..

• Lehtonen, Erkko; Pöschel, Reinhard; Waldhauser, Tamás (2018)  Reflections on and of minor-closed classes of multisorted operations . Algebra Universalis: 79, Art. 71, 19 pp..

• Couceiro, Miguel; Lehtonen, Erkko (2018)  Majors of functions . Order: 35, 233–246.

• Lehtonen, Erkko; Pöschel, Reinhard (2017)  Permutation groups, pattern involvement, and Galois connections . Acta Sci. Math. (Szeged): 83, 355–375.

• Couceiro, Miguel; Lehtonen, Erkko (2016)  On the arity gap of finite functions: results and applications . Journal of Multiple-Valued Logic and Soft Computing: 27, 193–207.

• Lehtonen, Erkko (2016)  On functions with a unique identification minor . Order: 33, 71–80.

• Lehtonen, Erkko; Pilitowska, Agata (2015)  Entropicity and generalized entropic property in idempotent n-semigroups . Semigroup Forum: 91, 260–281.

• Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten (2015)  A complete classification of equational classes of threshold functions included in clones . RAIRO Operations Research: 49, 39–66.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2015)  A survey on the arity gap . Journal of Multiple-Valued Logic and Soft Computing: 24, 223–249.

• Lehtonen, Erkko (2015)  Reconstructing permutations from identification minors . Electronic Journal of Combinatorics: 22(4), #P4.20.

• Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten (2015)  Hypomorphic Sperner systems and non-reconstructible functions . Order: 32, 255–292.

• Lehtonen, Erkko (2015)  On functions with a unique identification minor . Order.

• Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten (2015)  Set-reconstructibility of Post classes . Discrete Applied Mathematics: 187, 12–18.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2015)  On equational definability of function classes . J. Mult.-Valued Logic Soft Comput.: 24, 203–222.

• Lehtonen, Erkko (2014)  Totally symmetric functions are reconstructible from identification minors . The Electronic Journal of Combinatorics: 21(2), #P2.6.

• Lehtonen, Erkko; Marichal, Jean-Luc; Teheux, Bruno (2014)  Associative string functions . Asian-Eur. J. Math.: 7(4), 1450059, 18 pp..

• Lehtonen, Erkko (2014)  Reconstructing multisets over commutative groupoids and affine functions over nonassociative semirings . International Journal of Algebra and Computation: 24(1), 11-31.

• Lehtonen, Erkko; Pilitowska, Agata (2014)  Generalized entropy in expanded semigroups and in algebras with neutral element . Semigroup Forum: 88(3), 702–714.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2014)  Additive decomposition schemes for polynomial functions over fields . Novi Sad J. Math.: 44(2), 89–105.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2013)  Parametrized arity gap . Order: 30, 557-572.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2013)  Additive decomposability of functions over abelian groups . International Journal of Algebra and Computation: 23, 643-662.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2012)  The arity gap of order-preserving functions and extensions of pseudo-Boolean functions . Discrete Applied Mathematics: 160(4-5), 383-390.

• Behrisch, Mike; Couceiro, Miguel; Kearnes, Keith A.; Lehtonen, Erkko; Szendrei, Ágnes (2012)  Commuting polynomial operations of distributive lattices . Order: 29(2), 245-269.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2012)  Decompositions of functions based on arity gap . Discrete Mathematics: 312(2), 238-247.

• Couceiro, Miguel; Lehtonen, Erkko (2012)  Galois theory for sets of operations closed under permutation, cylindrification, and composition . Algebra Universalis: 67(3), 273-297.

• Kwuida, Léonard; Lehtonen, Erkko (2011)  On the homomorphism order of labeled posets . Order: 28, 251-265.

• Couceiro, Miguel; Lehtonen, Erkko (2011)  Self-commuting lattice polynomial functions on chains . Aequationes mathematicae: 81(3), 263-278.

• Lehtonen, Erkko; Szendrei, Ágnes (2011)  Clones with finitely many relative R-classes . Algebra Universalis: 65, 109-159.

• Lehtonen, Erkko; Szendrei, Ágnes (2010)  The submaximal clones on the three-element set with finitely many relative R-classes . Discussiones Mathematicae - General Algebra and Applications: 30(1), 7-33.

• Lehtonen, Erkko (2010)  Closed classes of functions, generalized constraints, and clusters . Algebra Universalis: 63(2-3), 203-234.

• Lehtonen, Erkko (2010)  A note on minors determined by clones of semilattices . Novi Sad Journal of Mathematics: 40(3), 75-81.

• Lehtonen, Erkko; Nešetril, Jaroslav (2010)  Minors of Boolean functions with respect to clique functions and hypergraph homomorphisms . European Journal of Combinatorics: 31(8), 1981-1995.

• Lehtonen, Erkko (2010)  Characterization of preclones by matrix collections . Asian-European Journal of Mathematics: 3(3), 457-473.

• Foldes, Stephan; Lehtonen, Erkko (2010)  Column-partitioned matrices over rings without invertible transversal submatrices . Ars Combinatoria: 97, 33-39.

• Couceiro, Miguel; Lehtonen, Erkko (2009)  Generalizations of Swierczkowski's lemma and the arity gap of finite functions . Discrete Mathematics: 309(20), 5905-5912.

• Lehtonen, Erkko; Szendrei, Ágnes (2009)  Equivalence of operations with respect to discriminator clones . Discrete Mathematics: 309(4), 673-685.

• Lehtonen, Erkko (2008)  Labeled posets are universal . European J. Combin.: 29, 493-506.

• Couceiro, Miguel; Lehtonen, Erkko (2007)  On the effect of variable identification on the essential arity of functions on finite sets . Int. J. Found. Comput. Sci.: 18, 975-986.

• Lehtonen, Erkko (2006)  Descending chains and antichains of the unary, linear, and monotone subfunction relations . Order: 23, 129-142.

• Couceiro, Miguel; Foldes, Stephan; Lehtonen, Erkko (2006)  Composition of Post classes and normal forms of Boolean functions . Discrete Math.: 306, 3223-3243.

• Lehtonen, Erkko; Waldhauser, Tamás ()  Associative spectra of graph algebras II. Satisfaction of bracketing identities, spectrum dichotomy . Journal of Algebraic Combinatorics.

Papers or Chapters in Edited Books

• Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten (2013)  Sur des classes de fonctions à seuil caractérisables par des contraintes relationnelles — On classes of threshold functions characterizable by relational constraints . Actes des 22èmes rencontres francophones sur la Logique Floue et ses Applications (LFA 2013), Université de Reims Champagne-Ardenne, 145-152.

• Lehtonen, Erkko; Szendrei, Ágnes (2012)  Partial orders induced by quasilinear clones . Proceedings of the Salzburg Conference 2011 (AAA81), Verlag Johannes Heyn, Klagenfurt, 51-84.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2011)  On the arity gap of aggregation functions . Decision Theory: Qualitative and Quantitative Approaches, Johannes Kepler Universität, Linz, 25–28.

• Couceiro, Miguel; Lehtonen, Erkko; Marichal, Jean-Luc; Waldhauser, Tamás (2011)  An algorithm for producing median formulas for Boolean functions . Proceedings of the Reed–Muller 2011 Workshop, Tampere International Center for Signal Processing (TICSP), 49-54.

• Couceiro, Miguel; Lehtonen, Erkko (2010)  The arity gap of polynomial functions over bounded distributive lattices . Proceedings of the 40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010), IEEE Computer Society, Los Alamitos, 113-116.

• Couceiro, Miguel; Lehtonen, Erkko (2010)  Explicit descriptions of bisymmetric Sugeno integrals . Computational Intelligence for Knowledge-Based Systems Design, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg: 6178, 494-501.

• Couceiro, Miguel; Lehtonen, Erkko (2010)  Classes of operations closed under permutation, cylindrification and composition . Proceedings of the 40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010), IEEE Computer Society, Los Alamitos, 117-121.

• Couceiro, Miguel; Lehtonen, Erkko (2008)  On the arity gap of finite functions: results and applications . Proceedings of the First International Conference on Relations, Orders and Graphs: Interaction with Computer Science (ROGICS ’08), Nouha Editions, Sfax, 65-72.

• Lehtonen, Erkko (2006)  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, 145-148.

• Couceiro, Miguel; Foldes, Stephan; Lehtonen, Erkko (2005)  On the complexity of representing sets of vertices in the n-cube . ICNAAM 2005, Wiley-VCH, Weinheim, 876-877.

• Couceiro, Miguel; Foldes, Stephan; Lehtonen, Erkko (2004)  On compositions of clones of Boolean functions . International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004), VSP/Brill, Utrecht, 849-851.

Communications in Conference Proceedings

• Couceiro, Miguel; Lehtonen, Erkko (2020)  Linearly definable classes of Boolean functions . Proceedings of the 1st International Conference on Algebras, Graphs and Ordered Sets (ALGOS 2020), 39–46.

• Couceiro, Miguel; Lehtonen, Erkko; Miclet, Laurent; Prade, Henri; Richard, Gilles (2020)  When nominal analogical proportions do not fail . Scalable Uncertainty Management, SUM 2020, Lecture Notes in Computer Science 12322, Springer, Cham, 68–83.

• Lehtonen, Erkko; Waldhauser, Tamás (2017)  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, 43–48.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2012)  Gap vs. pag . Proceedings of the 42nd IEEE International Symposium on Multiple-Valued Logic (ISMVL 2012), IEEE Computer Society, Los Alamitos, 268-273.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2011)  A survey on the arity gap . Proceedings of 41-st IEEE International Symposium on Multiple-Valued Logic (ISMVL 2011), IEEE Computer Society, Los Alamitos, 277-281.

• Couceiro, Miguel; Lehtonen, Erkko; Waldhauser, Tamás (2011)  On equational definability of function classes . Proceedings of the 41st IEEE International Symposium on Multiple-Valued Logic (ISMVL 2011), IEEE Computer Society, Los Alamitos, 182-186.

Thesis

• Lehtonen, Erkko (2018)  Reconstruction of functions from minors . habilitation thesis, Technische Universität Dresden, Dresden.

• Lehtonen, Erkko (2007)  Operations on Finite Sets, Functional Composition, and Ordered Sets . doctoral dissertation, Tampere University of Technology, Publication 680, Tampere.