منابع مشابه
The Flagged Cauchy Determinant
We consider a flagged form of the Cauchy determinant, for which we provide a combinatorial interpretation in terms of nonintersecting lattice paths. In combination with the standard determinant for the enumeration of nonintersecting lattice paths, we are able to give a new proof of the Cauchy identity for Schur functions. Moreover, by choosing different starting and end points for the lattice p...
متن کاملLattice Paths and the Flagged Cauchy Determinant
We obtain a flagged form of the Cauchy determinant and establish a correspondence between this determinant and nonintersecting lattice paths, from which it follows that Cauchy identity on Schur functions. By choosing different origins and destinations for the lattice paths, we are led to an identity of Gessel on the Cauchy sum of Schur functions in terms of the complete symmetric functions in t...
متن کاملThe Flagged Double Schur Function
The double Schur function is a natural generalization of the factorial Schur function introduced by Biedenharn and Louck. It also arises as the symmetric double Schubert polynomial corresponding to a class of permutations called Grassmannian permutations introduced by A. Lascoux. We present a lattice path interpretation of the double Schur function based on a flagged determinantal definition, w...
متن کاملFlagged Higher Categories
We introduce flagged (∞, n)-categories and prove that they are equivalent to Segal sheaves on Joyal’s category Θn. As such, flagged (∞, n)-categories provide a model-independent formulation of Segal sheaves. This result generalizes the statement that n-groupoid objects in spaces are effective, as we explain and contextualize. Along the way, we establish a useful expression for the univalent-com...
متن کاملA Determinant of the Chudnovskys Generalizing the Elliptic Frobenius-Stickelberger-Cauchy Determinantal Identity
D.V. Chudnovsky and G.V. Chudnovsky [CH] introduced a generalization of the FrobeniusStickelberger determinantal identity involving elliptic functions that generalize the Cauchy determinant. The purpose of this note is to provide a simple essentially non-analytic proof of this evaluation. This method of proof is inspired by D. Zeilberger’s creative application in [Z1]. AMS Subject Classificatio...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2005
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-004-0593-9