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A generalization and proof of the AanderaaRosenberg conjecture
 PROC. 7TH SIGACT CONFERENCE
, 1975
"... We investigate the maximum number C(P) of arguments of P that must be tested in order to compute P, a Boolean function of d Boolean arguments. We present evidence for the general conjecture that C(P) = d whenever P(O d) ~ P(l d) and P is left invariant by a transitive permutation group acting on ..."
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Cited by 12 (1 self)
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on the arguments. A nonconstructive argument (not based on the construction of an "oracle") proves the generalized conjecture for d a prime power. We use this result to prove the AanderaaRosenberg conjecture by showing that at least v2/9 entries of the adjacency matrix of a vvertex undirected graph G
The Use of Explicit Plans to Guide Inductive Proofs
 9TH CONFERENCE ON AUTOMATED DEDUCTION
, 1988
"... We propose the use of explicit proof plans to guide the search for a proof in automatic theorem proving. By representing proof plans as the specifications of LCFlike tactics, [Gordon et al 79], and by recording these specifications in a sorted metalogic, we are able to reason about the conjectures ..."
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Cited by 295 (40 self)
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the conjectures to be proved and the methods available to prove them. In this way we can build proof plans of wide generality, formally account for and predict their successes and failures, apply them flexibly, recover from their failures, and learn them from example proofs. We illustrate this technique
Proof of a conjecture of Whitney
 Pacific J. Math
, 1969
"... Let M be a closed, connected, nonorientable surface of Euler characteristic X which is smoothly embedded in Euclidean 4space, R4, with normal bundle v. The Euler class of i>, denoted by e(v), is an element of the cohomology group H2(M; %) (the letter % denotes twisted integer coefficients). Sin ..."
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Cited by 23 (0 self)
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to give a proof of this conjecture of Whitney. The proof depends on a corollary of the AtiyahSinger index theorem. This corollary is concerned with manifolds with an orientation preserving involution; an elementary proof of the corollary has recently been given by K. Janϊch and E Ossa, [5]. The author
A Proof of the Hodge Conjecture
"... In this paper we show that the Hodge conjecture and a part of the Tate conjecture hold. Since it is difficult to find algebraic cycles in general, the strategy is to proceed by induction argument to vanish a certain subspace of a cohomology of an open affine subvariety of an affine variety which is ..."
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In this paper we show that the Hodge conjecture and a part of the Tate conjecture hold. Since it is difficult to find algebraic cycles in general, the strategy is to proceed by induction argument to vanish a certain subspace of a cohomology of an open affine subvariety of an affine variety which
Proof of the BrlekReutenauer conjecture
, 2013
"... a b s t r a c t Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = , where C u and P u are the factor and palindromic complexity of u, respectively. This conjecture was verified for periodic words by Brlek and Reutenauer th ..."
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Cited by 1 (0 self)
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themselves. Using their results for periodic words, we have recently proved the conjecture for uniformly recurrent words. In the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words.
A proof of the HoggattBergum conjecture
, 1999
"... It is proved that if k and d are positive integers such that the product of any two distinct elements of the set {F_2k , F_2k+2 , F_2k+4 , d} increased by 1 is a perfect square, than d has to be 4F_2k+1 F_ 2k+2 F_2k+3. This is a generalization of the theorem of Baker and Davenport for k = 1. ..."
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Cited by 17 (10 self)
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It is proved that if k and d are positive integers such that the product of any two distinct elements of the set {F_2k , F_2k+2 , F_2k+4 , d} increased by 1 is a perfect square, than d has to be 4F_2k+1 F_ 2k+2 F_2k+3. This is a generalization of the theorem of Baker and Davenport for k = 1.
A proof for a generalized Nakayama conjecture
, 2005
"... In a recent paper Külshammer, Olsson, and Robinson proved a deep generalization of the Nakayama conjecture for symmetric groups. We provide a similar but a shorter and relatively elementary proof of their result. Our method enables us to obtain a more general Hanalogue of the Nakayama conjecture w ..."
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Cited by 3 (1 self)
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In a recent paper Külshammer, Olsson, and Robinson proved a deep generalization of the Nakayama conjecture for symmetric groups. We provide a similar but a shorter and relatively elementary proof of their result. Our method enables us to obtain a more general Hanalogue of the Nakayama conjecture
A simple proof for the generalized Frankel conjecture
, 2007
"... In this short paper, we will give a simple and transcendental proof for Mok’s theorem of the generalized Frankel conjecture. This work is based on the maximum principle in [4] proposed by Brendle and Schoen. ..."
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Cited by 3 (1 self)
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In this short paper, we will give a simple and transcendental proof for Mok’s theorem of the generalized Frankel conjecture. This work is based on the maximum principle in [4] proposed by Brendle and Schoen.
Simple proof of a generalization of Deligne’s conjecture
"... Abstract. The goal of this paper is to give a simple proof of Deligne’s conjecture (proven by Fujiwara) and to generalize it to the situation appearing in our joint project [KV] with David Kazhdan on the global Langlands correspondence over function fields. Our proof applies without any changes to m ..."
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Cited by 4 (1 self)
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Abstract. The goal of this paper is to give a simple proof of Deligne’s conjecture (proven by Fujiwara) and to generalize it to the situation appearing in our joint project [KV] with David Kazhdan on the global Langlands correspondence over function fields. Our proof applies without any changes
Proof of Polyakov conjecture for general elliptic singularities 1
, 2001
"... A proof is given of Polyakov conjecture about the accessory parameters of the SU(1,1) RiemannHilbert problem for general elliptic singularities on the Riemann sphere. Its relevance to 2 + 1 dimensional gravity is stressed. 1 ..."
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A proof is given of Polyakov conjecture about the accessory parameters of the SU(1,1) RiemannHilbert problem for general elliptic singularities on the Riemann sphere. Its relevance to 2 + 1 dimensional gravity is stressed. 1
Results 1  10
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