Reconstructing functions of several arguments from identification minors
16/12/2013 Segundafeira, 16 de Dezembro de 2013, 16h0017h00, IIIULAnfiteatro
Erkko Lehtonen (University of Luxembourg)
Institute for Interdisciplinary Research  University of Lisbon
This talk deals with the problem whether a function $f \colon A^n \to B$ can be reconstructed from its identification minors, i.e., functions derived from $f$ by identifying a pair of its arguments. Some recent results, both positive and negative, about this reconstruction problem are discussed (see [1, 2, 3, 4]). For example, totally symmetric functions and affine functions over finite fields are reconstructible. On the other hand, the class of orderpreserving functions is not reconstructible. Some open problems are also presented.
References:
[1] E. Lehtonen, On the reconstructibility of totally symmetric functions and of other functions with a unique identification minor, arXiv:1208.3110.
[2] E. Lehtonen, Reconstructing multisets over commutative groupoids, with an application to a reconstruction problem for functions of several arguments (the case of affine functions), arXiv:1302.7109.
[3] M. Couceiro, E. Lehtonen, K. Schölzel, Hypomorphic Steiner systems and nonreconstructible functions, arXiv:1306.5578.
[4] M. Couceiro, E. Lehtonen, K. Schölzel, Setreconstructibility of Post classes, arXiv:1310.7797.
