The calculation of the adjacency indices of type $D$ singularities of a front

TL;DR

This paper derives a formula to calculate the adjacency indices of type D singularities to multisingularities of type A, providing a method to count specific strata in the discriminant of real simple singularities.

Contribution

It introduces a new formula for calculating adjacency indices of D-type singularities to A-type multisingularities in real simple singularities.

Findings

Formula for adjacency indices of D_mu^± to A_mu_1^{k_1}...A_mu_p^{k_p}

Number of strata of a given A-type in the discriminant of D-type singularities

Application to real simple singularities

Abstract

The formula for the calculation of the adjacency indices of types $D_\mu^\pm$ Legendrian monosingularities to multisingularities of types $A_{\mu_1}^{k_1}\dots A_{\mu_p}^{k_p}$ is obtained in the paper. Namely the number of strata of a given type $A_{\mu_1}^{k_1}\dots A_{\mu_p}^{k_p}$ in the discriminant of a real simple singularity of any of types $D_\mu^\pm$ is calculated.