Combinatorial exploration : an algorithmic framework for enumeration / Michael H. Albert, Christian Bean, Anders Claesson, Émile Nadeau, Jay Pantone, Henning Ulfarsson.

Format:

Book

Author/Creator:

Albert, Michael H., author.

Bean, Christian, author.

Claesson, Anders, author.

Nadeau, Émile, author.

Pantone, Jay, author.

Ulfarsson, Henning, author.

Series:

Memoirs of the American Mathematical Society ; volume 317, number 1611.

Memoirs of the American Mathematical Society, 0065-9266 ; volume 317, number 1611

Language:

English

Subjects (All):

Combinatorial analysis.

Physical Description:

v, 109 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2026.

Summary:

Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and provide an open-source Python implementation. As a prerequisite, we build up a new theoretical foundation for combinatorial decomposition strategies and combinatorial specifications. We then apply Combinatorial Exploration to the domain of permutation patterns, to great effect. We rederive hundreds of results in the literature in a uniform manner and prove many new ones. These results can be found in a new public database, the Permutation Pattern Avoidance Library (PermPAL) at https://permpal.com. Finally, we give three additional proofs-of-concept, showing examples of how Combinatorial Exploration can prove results in the domains of alternating sign matrices, polyominoes, and set partitions.

Notes:

Includes bibliographical references (pages 103-109).

ISBN:

147048000X

9781470480004

OCLC:

1579211772