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Using either the RSK correspondence or the [PHI] correspondence, the Cauchy formula (1) can be interpreted as a bijection between monomials on the left hand side and pairs of SSYTs or SSAFs on the right.
The Cauchy formula which relates perimeter and number of intercepts provides a simple method for perimeter computation (Serra, 1982).
rewrite it in the form of the Cauchy formula by introducing the correct
Zampieri takes graduate students through the material in remarkably gentle fashion, first covering complex variables such as Cauchy formulas in polydiscs, Levi forms and the logarithmic supermean of the Taylor radius of holomorphic functions, real structures, including Euclidean spaces, real synthetic spaces (the Frobenius-Darboux theorem), and real/complex structures such as CR manifolds and mappings, real/complex symplectic spaces, iterated commutators (Bloom-Graham normal forms) and separate real analyticity.