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accents for Turán and simplified/standardized link
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user9072
user9072

A simple proof for a theorem of Szekeres and TuranTurán

Szekeres and TuranTurán found in 1937 a formula for the sum of the squares and the sum of the fourth powers of determinants of all $n$ by $n$ matrices with $\pm 1$ entries. (The sum of squares case follows easily from Cauchy-Binet identity.) Later TuranTurán publishedpublished a simpler proof for the sum of the fourth powers but in Chinese. I vaguely remember that there are simpler probabilistic proofs for both cases.

My question is about simple proofs for these identities, especially the one for 4th powers.

Is there a formula for the 6th power?

A simple proof for a theorem of Szekeres and Turan

Szekeres and Turan found in 1937 a formula for the sum of the squares and the sum of the fourth powers of determinants of all $n$ by $n$ matrices with $\pm 1$ entries. (The sum of squares case follows easily from Cauchy-Binet identity.) Later Turan published a simpler proof for the sum of the fourth powers but in Chinese. I vaguely remember that there are simpler probabilistic proofs for both cases.

My question is about simple proofs for these identities, especially the one for 4th powers.

Is there a formula for the 6th power?

A simple proof for a theorem of Szekeres and Turán

Szekeres and Turán found in 1937 a formula for the sum of the squares and the sum of the fourth powers of determinants of all $n$ by $n$ matrices with $\pm 1$ entries. (The sum of squares case follows easily from Cauchy-Binet identity.) Later Turán published a simpler proof for the sum of the fourth powers but in Chinese. I vaguely remember that there are simpler probabilistic proofs for both cases.

My question is about simple proofs for these identities, especially the one for 4th powers.

Is there a formula for the 6th power?

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Gil Kalai
Gil Kalai
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A simple proof for a theorem of Szekeres and Turan

Szekeres and Turan found in 1937 a formula for the sum of the squares and the sum of the fourth powers of determinants of all $n$ by $n$ matrices with $\pm 1$ entries. (The sum of squares case follows easily from Cauchy-Binet identity.) Later Turan published a simpler proof for the sum of the fourth powers but in Chinese. I vaguely remember that there are simpler probabilistic proofs for both cases.

My question is about simple proofs for these identities, especially the one for 4th powers.

Is there a formula for the 6th power?