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On the generating function and growth of the positive singular braid monoid

A. L. Anisimov, G. A. Kameneva, V. V. Vershinin

Abstract

We prove that the generating function of the positive singular braid monoid is rational and we give the exact formula for such monoid on three strands.

On the generating function and growth of the positive singular braid monoid

Abstract

We prove that the generating function of the positive singular braid monoid is rational and we give the exact formula for such monoid on three strands.
Paper Structure (6 sections, 3 theorems, 39 equations, 1 figure)

This paper contains 6 sections, 3 theorems, 39 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Statements of the main results
  3. Proofs
  4. Proof of Theorem 1
  5. Proof of Theorem 2
  6. Growth

Key Result

Theorem 2.1

The generating function for the positive singular braid monoid $SB_n^+$ is rational.

Figures (1)

  • Figure 1.1: The singular braid generator $x_i$

Theorems & Definitions (3)

  • Theorem 2.1
  • Theorem 2.2
  • Corollary 2.3