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darij grinberg
darij grinberg
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The minors of a Vandermonde matrix are known as alternants. Their positivity follows from the fact that they are products of the Vandermonde determinant of the variables involved with a Schur function in these variables. For a short and self-contained proof of this fact, see "Corollary (The Bi-Alternant Formula)" in John R. Stembridge, A Concise Proof of the Littlewood-Richardson Rule, The Electronic Journal of Combinatorics 9 (2002), Note #N5John R. Stembridge, A Concise Proof of the Littlewood-Richardson Rule, The Electronic Journal of Combinatorics 9 (2002), Note #N5. This note itself is the distillate of several years of algebraic combinatorics (ideas of Lindstrom, Gessel, Viennot, Gasharov, Bender and Knuth are all in there), and longer proofs have been found before (e.g., in Macdonald's book).

The minors of a Vandermonde matrix are known as alternants. Their positivity follows from the fact that they are products of the Vandermonde determinant of the variables involved with a Schur function in these variables. For a short and self-contained proof of this fact, see "Corollary (The Bi-Alternant Formula)" in John R. Stembridge, A Concise Proof of the Littlewood-Richardson Rule, The Electronic Journal of Combinatorics 9 (2002), Note #N5. This note itself is the distillate of several years of algebraic combinatorics (ideas of Lindstrom, Gessel, Viennot, Gasharov, Bender and Knuth are all in there), and longer proofs have been found before (e.g., in Macdonald's book).

The minors of a Vandermonde matrix are known as alternants. Their positivity follows from the fact that they are products of the Vandermonde determinant of the variables involved with a Schur function in these variables. For a short and self-contained proof of this fact, see "Corollary (The Bi-Alternant Formula)" in John R. Stembridge, A Concise Proof of the Littlewood-Richardson Rule, The Electronic Journal of Combinatorics 9 (2002), Note #N5. This note itself is the distillate of several years of algebraic combinatorics (ideas of Lindstrom, Gessel, Viennot, Gasharov, Bender and Knuth are all in there), and longer proofs have been found before (e.g., in Macdonald's book).

Source Link
darij grinberg
darij grinberg
  • 33.8k
  • 4
  • 118
  • 253

The minors of a Vandermonde matrix are known as alternants. Their positivity follows from the fact that they are products of the Vandermonde determinant of the variables involved with a Schur function in these variables. For a short and self-contained proof of this fact, see "Corollary (The Bi-Alternant Formula)" in John R. Stembridge, A Concise Proof of the Littlewood-Richardson Rule, The Electronic Journal of Combinatorics 9 (2002), Note #N5. This note itself is the distillate of several years of algebraic combinatorics (ideas of Lindstrom, Gessel, Viennot, Gasharov, Bender and Knuth are all in there), and longer proofs have been found before (e.g., in Macdonald's book).