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- W4298430462 abstract "The number of Monotone Triangles with bottom row k1 < k2 < ... < kn is given by a polynomial alpha(n; k1,...,kn) in n variables. The evaluation of this polynomial at weakly decreasing sequences k1 >= k2 >= ... >= kn turns out to be interpretable as signed enumeration of new combinatorial objects called Decreasing Monotone Triangles. There exist surprising connections between the two classes of objects -- in particular it is shown that alpha(n; 1,2,...,n) = alpha(2n; n,n,n-1,n-1,...,1,1). In perfect analogy to the correspondence between Monotone Triangles and Alternating Sign Matrices, the set of Decreasing Monotone Triangles with bottom row (n,n,n-1,n-1,...,1,1) is in one-to-one correspondence with a certain set of ASM-like matrices, which also play an important role in proving the claimed identity algebraically. Finding a bijective proof remains an open problem." @default.
- W4298430462 created "2022-10-02" @default.
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- W4298430462 date "2012-01-01" @default.
- W4298430462 modified "2023-09-25" @default.
- W4298430462 title "Combinatorial Reciprocity for Monotone Triangles" @default.
- W4298430462 hasPublicationYear "2012" @default.
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