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Stanley's Zrank Problem on Skew Partitions
William Y. C. Chen, Arthur L. B. Yang
We present an affirmative answer to Stanley's zrank problem, namely, the zrank and rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices…
Stable Equivalences of Giambelli Type Matrices of Schur Functions
William Y. C. Chen, Arthur L. B. Yang
By using cutting strips and transformations on outside decompositions of a skew diagram, we show that the Giambelli type matrices of a skew Schur function are stably equivalent to…
The Zrank Conjecture and Restricted Cauchy Matrices
Guo-Guang Yan, Arthur L. B. Yang, Joan J. Zhou
The rank of a skew partition , denoted , is the smallest number such that is a disjoint union of border strips. Let denote the skew Sch…
Division and the Giambelli Identity
Susan Y. J. Wu, Arthur L. B. Yang
Given two polynomials f(x) and g(x), we extend the formula expressing the remainder in terms of the roots of these two polynomials to the case where f(x) is a Laurent polynomial. T…
Transformations of Border Strips and Schur Function Determinants
William Y. C. Chen, Guo-Guang Yan, Arthur L. B. Yang
We introduce the notion of the cutting strip of an outside decomposition of a skew shape, and show that cutting strips are in one-to-one correspondence with outside decompositions…