Percy Alexander MacMahon: Collected Papers

Title
Contents
Introduction
Bibliography of the Mathematical Papers of Percy Alexander MacMahon
13. Symmetric Functions of Several Systems of Quantities
13.1 Introduction and Commentary
13.2 Partition Identities and Invariants of Finite Groups, by. L. Solomon
13.3 Summary of the Paper
[34] Memoir on Symmetric Functions of the Roots of Systems of Equations
14. Determinants
14.1 Introduction and Commentary
14.2 References
14.3 Summaries of the Papers
[113] Researches in the theory of determinants
[115] On an X-determinant which includes as particular cases both “determinants” and “permanents"
[116] The symmetric functions of which the general determinant is a particular case
[120] The structure of a determinant
[121] The expansion of determinants and permanents in terms of symmetric functions
15. Repeating Patterns
15.1 Introduction and Commentary
15.2 Tiling the Plane with Congruent Pentagons, by D. Schattschneider
15.3 References
15.4 Summaries of the Papers
[44] On the thirty cubes that can be constructed with six differently colored squares
[98] (with W. P. D. MacMahon) The design of repeating patterns
[99] The design of repeating patterns for decorative work
[100] Pythagoras’s theorem as a repeating pattern
16. Multiplicative Number Theory
16.1 Introduction and Commentary
16.2 Fine’s Theorem
16.3 References
16.4 Summaries of the Papers
[92] The divisors of numbers
[93] Divisors of numbers and their continuations in the theory of partitions
[104] Congruences with respect to composite moduli
[112] Properties of prime numbers deduced from the calculus of symmetric functions
17. Analysis, Astronomy, Geometry, and Physics
17.1 Introduction and Commentary
17.2 References
17.3 Summaries of the Papers
[1] A property of pedal curves
[2] Sur un résultat de calcul obtenu par M. Allégret
[3] The Cassinian
[4] An extension of Steiner’s problem
[5] The three-cusped hypocycloid
[6] On a generalization of the nine-points properties of a triangle
[9] On the differential equation X^(-2/3) dx + Y^(-2/3) dy + Z^(-2/3) dz = 0
[55] Mirage
[72] The determination of the apparent diameter of a fixed star
[90] (with H. B. C. Darling) Reciprocal relations in the theory of integral equations
[91] (with H. B. C. Darling) Contribution to the theory of attraction when the force varies as any power of the distance
[106] On a class of transcendents of which the Bessel functions are a particular case
18. Invariant Theory
18.1 Introduction and Commentary
18.2 A Letter from A. C. Aitken to an Edinburgh Colleague
18.3 References
18.4 Summaries of the Papers
[8] On Professor Cayley’s canonical form
[13] Seminvariants and symmetric functions
[14] Symmetric functions of the 13-ic
[18] On perpetuants
[19] Operators in the theory of seminvariants
[21] Memoir on seminvariants
[22] On perpetuant reciprocants
[23] The theory of a multilinear partial differential operator, with applications to the theories of invariants and reciprocants
[24] The differential equation of the most general substitution of one variable
[26] Observations on the generating functions of the theory of invariants
[27] The expression of syzygies among perpetuants by means of partitions
[29] The algebra of multilinear partial differential operators
[30] The eliminant of two binary quantics
[36] A theorem in the calculus of linear partial differential operators
[47] The perpetuant invariants of binary quantics
[63] On the application of quaternions to the orthogonal transformation and invariant theory
[64] Seminvariants of systems of binary quantics, the order of each quantic being infinite
[69] Memoir on the orthogonal and other special systems of invariants
[70] Preliminary note on the operational invariants of a binary quantic
[80] The operator reciprocants of Sylvester’s theory of reciprocants
[84] The invariants of the Halphenian homographic substituion _ to which is appended some investigations concerning the transformation of differential operators which present themselves in invariant theory
[85] On a modified form of pure reciprocants possessing the property that the algebraical sum of the coefficients is zero
19. Expository Papers
19.1 Introduction and Commentary
19.2 Summaries of the Papers
[37] Weighing by a series of weights
[49] Combinatory analysis: a review of the present state of knowledge (presidential address)
[50] James Joseph Sylvester
[59] Presidential Address, Section A, British Association
[60] Magic squares and other problems upon a chess board
[74] Algebraic forms
[75] Arthur Cayley
[76] Combinatorial analysis
20. Obituaries
20.1 Percy Alexander MacMahon by H. F. Baker
20.2 Percy Alexander MacMahon by H. H. Turner
Contents of Volume I