منابع مشابه
A short WZ-style proof of Abel's identity
Using a certification procedure for Abel-type sums, we present a computerized proof of Abel’s identity. Abel’s identity [1],[2] can be proved in many ways, including the elegant combinatorial methods of [3]. Here we present the first computer-generated proof using the methods introduced in [4]. Theorem([1]; [2], p.128). For n ≥ 0:
متن کاملA SHORT PROOF OF A RESULT OF NAGEL
Let $(R,fm)$ be a Gorenstein local ring and$M,N$ be two finitely generated modules over $R$. Nagel proved that if $M$ and $N$ are inthe same even liaison class, thenone has $H^i_{fm}(M)cong H^i_{fm}(N)$ for all $iIn this paper, we provide a short proof to this result.
متن کاملA Short Proof of an Identity of Sylvester
We present two short proofs of an identity found by Sylvester and rediscovered by Louck. The first proof is an elementary version of Knuth’s proof and is analogous to Macdonald’s proof of a related identity of Milne. The second is Sylvester’s own proof of his identity.
متن کاملA short proof of the q-Dixon identity
We give a simple proof of Jackson’s terminating q-analogue of Dixon’s identity. In the last twenty years several short proofs of Dixon’s identity have been published [3–5]. However, there are not so many proofs of Jackson’s terminating q-analogue of Dixon’s identity [2, 6]: ∑ k (−1)kq(3k2+k)/2 [ a+ b a+ k ][ a+ c c+ k ][ b+ c b+ k ] = [a+ b+ c]! [a]![b]![c]! , (1) where [n]! = ∏n i=1 1−qi 1−q a...
متن کاملProof Style
We are concerned with how to communicate a mathematical proof to a computer theorem prover. This can be done in many ways, while allowing the machine to generate a completely formal proof object. The most obvious choice is the amount of guidance required from the user, or from the machine perspective, the degree of automation provided. But another important consideration, which we consider part...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1995
ISSN: 1077-8926
DOI: 10.37236/1274