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Dear Experts,

I'm a graduate student, dealing with group-theory.

In my current research, I used the bound "Alexander Gruber" wrote about in this post: See Here (Actually, I have just found out that the bound is known and already mentioned online).

I was able to give a detailed proof for this claim myself of course , but since it seems like this bound is well known, I want to add a reference .

So... does anyone know about a reference for the bound Alexander Gruber gives in the post above? I want to add it to the Bibliography section.

Thanks for your help!

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1 Answer 1

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For general Hall Algebra,

Ian MacDonald's Symmetric Functions and Hall Polynomials http://books.google.com.hk/books/about/Symmetric_Functions_and_Hall_Polynomials.html?id=srv90XiUbZoC

For general reference about the number of vector subspaces over a finite p-field,

I suggest that you can google the keyword "subspaces over a finite p-field", here're some papers and some related problems arise in StackExchange:

http://math.stackexchange.com/questions/70801/how-many-k-dimensional-subspaces-there-are-in-n-dimentional-vector-space-over

And a popular ref. is the Goldman's paper which may contain the bounds:

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, in \Recent progress in combinatorics" (W. Tutte, Ed.), pp. 75{83. Aca- demic Press, San Diego, CA, 1969.

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Thanks a lot! ! –  TheForumLord Apr 12 '13 at 17:42

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