منابع مشابه
Some Remarks on Sign-Balanced and Maj-Balanced Posets
Let P be an n-element poset (partially ordered set), and let ω : P → [n] = {1, 2, . . . , n} be a bijection, called a labeling of P . We call the pair (P, ω) a labelled poset. A linear extension of P is an order-preserving bijection f : P → [n]. We can regard f as defining a permutation π = π(f) of the set [n] given by π(i) = j if f(ω(j)) = i. We write π in the customary way as a word a1a2 · · ...
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We start with a combinatorial definition of I-sign types which are a generalization of the sign types indexed by the root system of type Al (I ⊂ N finite). Then we study the set DI p of I-sign types associated to the partial orders on I. We establish a 1-1 correspondence between D [n] p and a certain set of convex simplexes in a euclidean space by which we get a geometric distinction of the sig...
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We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance identities for partition shapes originally conjectured by Stanley, now proven in [4, 5, 7]. We show that these identities result from a signed differential poset...
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We study signed differential posets, a signed version of Stanley’s differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance identities for partition shapes originally conjectured by Stanley, now proven in [3, 4, 6]. We show that these identities result from a signed differen...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2001
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3146