%0 Journal Article %T Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture %A Alexei D. Miasnikov %A Alexei G. Myasnikov %J Mathematics %D 2003 %I arXiv %X The Andrews-Curtis conjecture states that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of the elementary Nielsen transformations and conjugations. In this paper we describe all balanced presentations of the trivial group on two generators and with the total length of relators <= 12. We show that all these presentations satisfy the Andrews-Curtis conjecture. %U http://arxiv.org/abs/math/0304305v1