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Graduate Texts in Mathematics #203
The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions
This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH
- GenresMathematicsAlgebra
256 pages, Hardcover
First published February 28, 1991
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Displaying 1 of 1 review
March 24, 2019
I refuse to tolerate any mathematician who says "All of science"---get over yourself---but these specialty topics (jeu de taquin, schur lemma, group characters) are ably covered and deserve wider recognition.
(((
By the way, ETS (the people who process childrens' test scores to prevent them from getting ahead in life) don't know this material, and should. Read upon linking, aligning, scores, scaling, Rasch models, and "equating", and you'll find that there's nothing to it but nonparametric guesswork bullshit. The theory of the symmetric group is quite deep but expositions of it are, unfortunately, hidden away.
The chances that psychometricians will read this review and act on my advice are nil, so prepare for another century of your kids' test scores based in pseudoscience.
)))
That said, Sagan covers a ton of interesting material. Who knows if it will apply to your area, but
The symmetric group as a topic demonstrates what mathematics is like generally. Technically, the symmetric group is "just a" subset of linear algebra, considering 0/1 matrices which are almost entirely sparse except for a single 1 in each row/column, like:
0 1 0
1 0 0
0 0 1
. However, contemplating the general linear group as shuffles, and asking how these could be, e.g., factored, leads somewhere entirely different.
Interesting subject matter, writing leaves much to be desired.
(((
By the way, ETS (the people who process childrens' test scores to prevent them from getting ahead in life) don't know this material, and should. Read upon linking, aligning, scores, scaling, Rasch models, and "equating", and you'll find that there's nothing to it but nonparametric guesswork bullshit. The theory of the symmetric group is quite deep but expositions of it are, unfortunately, hidden away.
The chances that psychometricians will read this review and act on my advice are nil, so prepare for another century of your kids' test scores based in pseudoscience.
)))
That said, Sagan covers a ton of interesting material. Who knows if it will apply to your area, but
The symmetric group as a topic demonstrates what mathematics is like generally. Technically, the symmetric group is "just a" subset of linear algebra, considering 0/1 matrices which are almost entirely sparse except for a single 1 in each row/column, like:
0 1 0
1 0 0
0 0 1
. However, contemplating the general linear group as shuffles, and asking how these could be, e.g., factored, leads somewhere entirely different.
Interesting subject matter, writing leaves much to be desired.
Displaying 1 of 1 review