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Study of the Integrability Property of Invariants of Combinatorial Structures

Student: Evgeny Krasilnikov

Supervisor: Sergei Lando

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Master)

Year of Graduation: 2019

We prove that the generating function for the Hopf algebra of framed graphs satisfies (after the appropriate rescaling of variables) the Kadomtsev–Petviashvili integrable hierarchy. Moreover, we verify that the similar statement for the Hopf algebras of weighted ghraphs, chord diagrams, binary delta-matroids, 3-hypergraphs and some others can not be formulated.

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