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This is an extended abstract of the talk given at the Oberwolfach Workshop"Algebraic Structures in Low-Dimensional Topology", 25 May -- 31 May 2014. Mygoal was to describe progress in distributive homology from the previousOberwolfach Workshop June 3 - June 9, 2012, in particular my work onYang-Baxter homology; however I concentrated my talk on my recent discovery ofq-polynomial of a rooted tree; the appropriate topic as my talk was on May 30,2014, the 30 anniversary of the Jones polynomial, and the polynomial has itsroots in the Kauffman bracket approach to the Jones polynomial.

Progress in distributive homology: from q-polynomial of rooted trees to Yang-Baxter homology