Note an Inequality for Kruskal-macaulay Functions
نویسندگان
چکیده
BERNARDO M. ÁBREGO, SILVIA FERNÁNDEZ-MERCHANT, AND BERNARDO LLANO Abstract. Given integers k ≥ 1 and n ≥ 0, there is a unique way of writing n as n = ¡nk k ¢ + ¡ nk−1 k−1 ¢ + ... + ¡ n1 1 ¢ so that 0 ≤ n1 < · · · < nk−1 < nk. Using this representation, the KruskalMacaulay function of n is defined as mk (n) = ¡ nk−1 k−1 ¢ + ¡ nk−1−1 k−2 ¢ + ... + ¡ n1−1 0 ¢ . We show that if a ≥ 0 and a < mk+1 (n), then mk (a) +mk+1 (n− a) ≥ mk+1 (n) . As a corollary, we obtain a short proof of Macaulay’s Theorem.
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An Inequality for Kruskal-macaulay Functions
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