# A talk of prof. Zhicheng Gao from Carleton University, Canada

SpeakerProf. Zhicheng Gao (Carleton University, Canada)

Time3 : 30 – 4 : 30 p.m., 21st(Thur.) March, 2019

PlaceRoom 404, Building 20

TitleAsymptotic properties of compositions over finite groups

Abstract: Let γ be a finite additive group. An m-composition over γ is an m-tuple (g1,g2,,gm) over γ. It is called an m-composition of g if $\sum_{j=1}^m g_j = g$. A composition (gj) over S is called locally restricted if there is a positive integer σ such that any σ consecutive parts of  (gj) satisfy certain conditions. Locally restricted compositions over γ are associated with walks in a de Bruijin graph.Under certain aperiodic conditions, we will show that the asymptotic number of m-compositions of γ is independent of γ.We also show that the distribution of the number of occurrences of a set of subwords in such m-compositions is asymptotically normal with mean and variance proportional to m. The proofs use the transfer matrix, Kronecker product of matrices, and Perron-Frobenius theorem, and tools from analytic combinatorics.