منابع مشابه
The polytope of even doubly stochastic matrices
The polytope Q, of the convex combinations of the permutation matrices of order n is well known (Birkhoff’s theorem) to be the polytope of doubly stochastic matrices of order n. In particular it is easy to decide whether a matrix of order n belongs to Q,. . check to see that the entries are nonnegative and that all row and columns sums equal 1. Now the permutations z of { 1, 2, . . . . n} are i...
متن کاملOn the Volume of the Polytope of Doubly Stochastic Matrices
We study the calculation of the volume of the polytope Bn of n × n doubly stochastic matrices; that is, the set of real non-negative matrices with all row and column sums equal to one. We describe two methods. The first involves a decomposition of the polytope into simplices. The second involves the enumeration of “magic squares”, i.e., n×n non-negative integer matrices whose rows and columns a...
متن کاملConstant Term Methods in the Theory of Tesler matrices and Macdonald Polynomial Operators
ABSTRACT The Tesler matrices with hook sums (a1, a2, . . . , an) are non-negative integral upper triangular matrices, whose i diagonal element plus the sum of the entries in the arm of its (french) hook minus the sum of the entries in its leg is equal to ai for all i. In a recent paper [6], the second author expressed the Hilbert series of the Diagonal Harmonic modules as a weighted sum of the ...
متن کاملSome Facets of the Polytope of Even Permutation Matrices
We describe a class of facets of the polytope of convex combinations of the collection of even n × n permutation matrices. As a consequence, we prove the conjecture of Brualdi and Liu [4] that the number of facets of the polytope is not bounded by a polynomial in n.
متن کاملCombinatorics of Tesler matrices in the theory of parking functions and diagonal harmonics
In [J. Haglund, A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants, Adv. Math. 227 (2011) 2092-2106], the study of the Hilbert series of diagonal coinvariants is linked to combinatorial objects called Tesler matrices. In this paper we use operator identities from Macdonald polynomial theory to give new and short proofs of some of these results. We also ...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2016
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-016-0241-2