Version of 2026-07-02

Notes on the combinatorial fundamentals of algebra, 2 July 2026 (2026-07-02)

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 2nd of July 2026, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

This version differs from arXiv:2008.09862v3 in that a number of minor errors have been corrected.

The numbering has not changed since the "10th of January 2019" release (or since arXiv:2008.09862v1), but a few exercises have been added at the end of Chapter 6.

Version of 2026-05-07

Notes on the combinatorial fundamentals of algebra, 7 May 2026 (2026-05-07)

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 7th of May 2026, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

This version differs from arXiv:2008.09862v3 in that a number of typos have been corrected.

The numbering has not changed since the "10th of January 2019" release (or since arXiv:2008.09862v1), but a few exercises have been added at the end of Chapter 6.

Version of 2022-09-15

Notes on the combinatorial fundamentals of algebra, 15th of September 2022 (2022-09-15)

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 15th of September 2022, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

The numbering has not changed since the "10th of January 2019" release (or since arXiv:2008.09862v1), but a few exercises have been added at the end of Chapter 6.

version of 2022-05-26

Notes on the combinatorial fundamentals of algebra, 26th of May 2022 (2022-05-26)

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 26th of May 2022, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

The numbering has not changed since the "10th of January 2019" release (or since arXiv:2008.09862v1), but a few exercises have been added at the end of Chapter 6.

Version of 2022-05-23

Notes on the combinatorial fundamentals of algebra, 23rd of May 2022 (2022-05-23)

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 23rd of May 2022, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

The numbering has not changed since the "10th of January 2019" release (or since arXiv:2008.09862v1), but a few exercises have been added at the end of Chapter 6.

Version of 2022-05-14

Notes on the combinatorial fundamentals of algebra, 14th of May 2022 (2022-05-14)
A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 14th of May 2022, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

The numbering has not changed since the "10th of January 2019" release (or since arXiv:2008.09862v1), but a few exercises have been added at the end of Chapter 6.

Version of 2021-05-25

Notes on the combinatorial fundamentals of algebra, 25th of May 2021 (2021-05-25)

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 25th of May 2021, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

The numbering has not changed since the "10th of January 2019" release (or since arXiv:2008.09862v1), but a few exercises have been added at the end of Chapter 6.

Version of 2021-05-22

Notes on the combinatorial fundamentals of algebra, 22nd of May 2021 (2021-05-22)

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 22nd of May 2021, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

The numbering has not changed since the "10th of January 2019" release (or since arXiv:2008.09862v1).

Version of 10 January 2019

Notes on the combinatorial fundamentals of algebra, 10th of January 2019 (2019-01-10)

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 10th of January 2019, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).

Update: The PDF attached to this release is a minor update, made on December 5, 2019. The numbering has not changed, but errors have been corrected.

Version of 7 November 2018

Notes on the combinatorial fundamentals of algebra, 7th of November 2018

A self-contained and elementary introduction to permutations and determinants; also includes some basic material on binomial coefficients and recurrent sequences. Some 100 exercises with solutions, and some 20 more exercises without.

This is a frozen version, created on the 7th of November 2018, archived here so that it can be referenced. The version on http://www.cip.ifi.lmu.de/~grinberg/ (and in the actual repository) will probably see some updates (and the numbering will change).