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Book Sections Year : 2022

The Tutte polynomial of matroid perspectives

Emeric Gioan

Abstract

This chapter covers the Tutte polynomial of matroid perspectives. Matroid perspectives adapt the idea of morphisms to matroid theory. The Tutte polynomial of a matroid perspective is a three-variable generalization of the Tutte polynomial that shares many of its properties. Definition of matroid perspectives, or matroid strong maps. Tutte polynomial generalized to matroid perspectives and various expansions. Structural and enumerative properties in terms of subset activities when the ground set is linearly ordered. Extensions to matroid perspectives of classical counting results. Applications, evaluations, computational complexity, and related polynomials.
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lirmm-03868715 , version 1 (23-11-2022)

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Emeric Gioan. The Tutte polynomial of matroid perspectives. Handbook of the Tutte Polynomial and Related Topics, Chapter 28, Chapman and Hall/CRC, 18 p., 2022, ⟨10.1201/9780429161612⟩. ⟨lirmm-03868715⟩
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