منابع مشابه
On Differential Posets
We study differential posets, a family of partially ordered sets discovered by Richard Stanley. In the first half of this paper we present an introduction to poset theory as relevant to differential posets and theorems on the structure and combinatorial properties of differential posets, culminating in the explicit definition of a new differential poset. In the second half we focus on Young’s l...
متن کامل6 Signed Differential Posets and Sign - Imbalance
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...
متن کاملA geometry of information, I: Nerves, posets and differential forms
The main theme of this workshop (Dagstuhl seminar 04351) is ‘Spatial Representation: Continuous vs. Discrete’. Spatial representation has two contrasting but interacting aspects (i) representation of spaces’ and (ii) representation by spaces. In this paper we will examine two aspects that are common to both interpretations of the theme, namely nerve constructions and refinement. Representations...
متن کاملPlane posets, special posets, and permutations
We study the self-dual Hopf algebra HSP of special posets introduced by Malvenuto and Reutenauer and the Hopf algebra morphism from HSP to the Hopf algebra of free quasi-symmetric functions FQSym given by linear extensions. In particular, we construct two Hopf subalgebras both isomorphic to FQSym; the first one is based on plane posets, the second one on heap-ordered forests. An explicit isomor...
متن کاملSigned Posets
We define a new object, called a signed poset, that bears the same relation to the hyperoctahedral group B n (i.e., signed permutations on n letters), as do posets to the symmetric group S n. We then prove hyperoctahedral analogues of the following results: (1) the generating function results from the theory of P-partitions; (2) the fundamental theorem of finite distributive lattices (or Birkho...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1988
ISSN: 0894-0347
DOI: 10.2307/1990995