Signed ring families and signed posets

Signed 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...

Upper Binomial Posets and Signed Permutation Statistics

6 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...

Sheffer posets and r - signed permutations ∗ Richard EHRENBORG

We generalize the notion of a binomial poset to a larger class of posets, which we call Sheffer posets. There are two interesting subspaces of the incidence algebra of such a poset. These spaces behave like a ring and a module and are isomorphic to certain classes of generating functions. We also generalize the concept of R-labelings to linear edge-labelings, and prove a result analogous to a t...

A Note on the Homology of Signed Posets

Let S be a signed poset in the sense of Reiner [4]. Fischer [2] defines the homology of S, in terms of a partial ordering P(S) associated to S, to be the homology of a certain subcomplex of the chain complex of P(S). In this paper we show that if P(S) is Cohen-Macaulay and S has rank n, then the homology of S vanishes for degrees outside the interval [n/2, n].