Signed Posets

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...

N ov 2 00 6 SIGNED DIFFERENTIAL POSETS AND SIGN - IMBALANCE

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...

A signed analog of the Birkhoff transform

We construct a family of posets, called signed Birkhoff posets, that may be viewed as signed analogs of distributive lattices. Our posets are generally not lattices, but they are shown to posses many combinatorial properties corresponding to well known properties of distributive lattices. They have the additional virtue of being face posets of regular cell decompositions of spheres. We give a c...

Upper Binomial Posets and Signed Permutation Statistics

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...