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Let P be a poset, and let A be an element of its strict incidence algebra. Saks (SIAM J. Algebraic Discrete Methods 1 (1980) 211-215; Discrete Math. 59 (1986) 135-166) and Gansner (SIAM J. Algebraic Discrete Methods 2 (1981) 429-440) proved that the kth Dilworth number of P is less than or equal to the dimension of the nullspace of A k , and that there is some member of the strict incidence...
Simion has a conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. The conjecture concerns the unimodality of a sequence of these numbers where the sum of the length and width of each rectangle is a constant and where the partition is constant. This paper demonstrates this unimodality if the partition is self-conjugate or if the Ferrers...
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