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Description
Substitutional AnalysisThis classic monograph on representation theory and the symmetric group is suitable for advanced undergraduates and graduate students of mathematics. The Bulletin of the American Mathematical Society hailed Daniel Edwin Rutherford's treatment as "a long overdue account of Young's representation theory of the symmetric group," noting that "many of Young's complicated proofs have been simplified through a free use of mathematical induction." Starting
This classic monograph on representation theory and the symmetric group is suitable for advanced undergraduates and graduate students of mathematics. The Bulletin of the American Mathematical Society hailed Daniel Edwin Rutherford's treatment as "a long overdue account of Young's representation theory of the symmetric group," noting that "many of Young's complicated proofs have been simplified through a free use of mathematical induction."Starting with an elementary overview of the theory of the symmetric group, the book proceeds to an examination of Young's formula, followed by an introduction to the fundamental notion of a standard diagram. Subsequent chapters present the passage to orthogonal and natural representations. No prior knowledge of the general theory of group characters is assumed, and the author deduces the necessary theory for the symmetric group. The final chapter illustrates the substitutional aspect of the theory, and a helpful appendix and bibliography conclude the text.
Binding Type: Paperback
Publisher: Dover Publications
Published: 04/17/2013
ISBN: 9780486491202
Pages: 102
Weight: 0.50lbs
Size: 8.40h x 5.40w x 0.60d
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★★★★★ 5
Durable
Style: Fetch Balls (Pack of 2), Size: 3 inch
Very bouncy. I like the noise it makes when you throw it. Pretty durable. Good size. Dog loves to play with them. Good material. Easy to use.
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Reviewed in the United States on April 5, 2026
★★★★★ 4
My dog loves glowing fetch at night!
Style: Glow Balls (Pack of 3), Size: 2.5 inch
Fantastic. Sturdy. My dog loves them
Glow in the dark is great for fetch at night. I keep a flashlight with me because the glow doesn't last really long. But they charge very quickly and are really bright.
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Reviewed in the United States on February 22, 2026
★★★★★ 5
Indestructible
Style: Fetch Balls (Pack of 2), Size: 3 inch
These balls are indestructible! We have a lab and a lab mix and they CANNOT damage these balls. They love them for fetch and to just chew on them (slightly squishy, but NO damage). Best toys we have bought for them.
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Reviewed in the United States on April 19, 2026
★★★★★ 5
Great trial set. Just be careful throwing the orange one!
Style: Assorted Balls (Pack of 3), Size: 2.5 inch
Blue isn't that easy to see in the yard
White charges with bright light/UV and is truly a game changer for night-time fetch. Both dogs clearly favor it.
Orange is easy to see in the grass at day
They're 3 different weights as well, so double trial. I prefer medium for my big dogs, though light performs well too
The orange is HEAVY and unyielding. Do NOT throw it with a ball thrower. It could damage your house or knock your dog out. Seems tough though.
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Reviewed in the United States on January 16, 2026
★★★★★ 3
Not as good as chuck it anymore
Style: Fetch Balls (Pack of 10), Size: 2.5 inch
I have bought these before and the where just like the chuck it balls. These are not those balls. The are lighter and my dog has already cause damage to one
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Reviewed in the United States on March 16, 2026