See Enumerative Combinatorics, vol. Richard Stanley Hi, Jeanne! Robert Bryant Inequality with symmetric polynomials [closed]. This looks like a better fit for Math Stackexchange, because it's the kind of thing one learns from Olympiad problem books. Noam D. Elkies David Hill 1, 7 7 silver badges 12 12 bronze badges.
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Polynomial that is symmetric in some variables. There are none. Brendan McKay Generalizing the Fundamental Theorem of Symmetric Polynomials. I heard of three relatively recent works in that direction, taking different routes and arriving to interesting information about diagonal invariants. Third, there is a by Vladimir Dotsenko I finally got around to writing the promised details.
I tried to make this a bit instructive, I hope you still find it useful. First I will expand a bit on my comment above. A good reference is Stanley's article "Invariants of finite groups and their applications to combinatorics". There is a folklore theorem which first appeared in print in M.
Gjergji Zaimi I believe the answer to your question is yes. Florian Eisele 1, 1 1 gold badge 11 11 silver badges 12 12 bronze badges. Schur polynomial, change of variable. PDE characterisation of elementary symmetric functions? For your first question, here's a simple proof. Willie Wong Examples of specializations of elementary symmetric polynomials.
Harry Richman 1, 8 8 silver badges 19 19 bronze badges. Lev Borisov having put up a complete solution; I'll put up how far I got.
I'm feeling annoyed with myself David E Speyer k 10 10 gold badges silver badges bronze badges. Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions? You have touched a vast subject called invariant theory. A nice characterisation of the ring of Dima Pasechnik Symmetric polynomial separating points. Automorphisms of 2- 22, 8, 4 Designs I.
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Landgev, V. Lindner, C. Rodger, D. Mathon, A. The Existence of Simple S3 3, 4, v K. Phelps, D. Stinson, S. On Combinatorial Designs with Subdesigns R. Rees, D.
Handbook of Enumerative Combinatorics - CRC Press Book
Sharry, A. Minimal Pairwise Balanced Designs R. Haim Hanani pioneered the techniques for constructing designs and the theory of pairwise balanced designs, leading directly to Wilson's Existence Theorem. He also led the way in the study of resolvable designs, covering and packing problems, latin squares, 3-designs and other combinatorial configurations. The Hanani volume is a collection of research and survey papers at the forefront of research in combinatorial design theory, including Professor Hanani's own latest work on Balanced Incomplete Block Designs.
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Other areas covered include Steiner systems, finite geometries, quasigroups, and t-designs. We are always looking for ways to improve customer experience on Elsevier. We would like to ask you for a moment of your time to fill in a short questionnaire, at the end of your visit. If you decide to participate, a new browser tab will open so you can complete the survey after you have completed your visit to this website. Thanks in advance for your time.
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Imprint: North Holland. Published Date: 11th October