Гафниан некоторых трехпараметрических теплицевых матриц и совершенные паросочетания дуговых и хордовых диаграмм

Abstract

We obtain an explicit formula for exact calculatingthe hafnian of 3-parameter Toeplitz matrices of aspecial type in polynomial time. We also give anasymptotic estimate for the hafnian of this type ofmatrices. Separately, we consider a case of non-negativeinteger parameters, when calculating the hafnianis equivalent to enumerating perfect matchings of arc and chord diagrams.