We exhibit a canonical connection between maximal (0, 1)-fillings of a moon polyomino avoiding northeast chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable and thus a shellable sphere. In particular, this implies a positivity result for Schubert polynomials. For ...

The Dushnik-Miller dimension of a poset ≤ is the minimal number d of linear extensions ≤1, . . . ,≤d of ≤ such that ≤ is the intersection of ≤1, . . . ,≤d. Supremum sections are simplicial complexes introduced by Scarf [13] and are linked to the Dushnik-Miller as follows: the inclusion poset of a simplicial complex is of Dushnik-Miller dimension at most d if and only if it is included in a supr...

R. S. Deodhar and M. K. Srinivasan defined a weight statistic on the set of involutions in the symmetric group and proved several results about the properties of this weight. These results include a recursion for a weight generating function, that the weight provides a grading for the set of fixed-point free involutions under a partial order related to the Bruhat partial order, and that this gr...

Let S be a finite alphabet. An injective word over S is a word over S such that each letter in S appears at most once in the word. We study Boolean cell complexes of injective words over S and their commutation classes. This generalizes work by Farmer and by Björner and Wachs on the complex of all injective words. Specifically, for an abstract simplicial complex ∆, we consider the Boolean cell ...

We consider a class of hypergraphs called hypercycles and we show that a hypercycle $C_n^{d,alpha}$ is shellable or sequentially the Cohen--Macaulay if and only if $nin{3,5}$. Also, we characterize Cohen--Macaulay hypercycles. These results are hypergraph versions of results proved for cycles in graphs.

We study the quotient complex ∆(B lm)/S l ≀ Sm as a means of deducing facts about the ring k[x 1 ,. .. , x lm ] S l ≀Sm. It is shown in [He] that ∆(B lm)/S l ≀ Sm is shellable when l = 2, implying Cohen-Macaulayness of k[x 1 ,. .. , x 2m ] S 2 ≀Sm for any field k. We now confirm for all pairs (l, m) with l > 2 and m > 1 that ∆(B lm)/S l ≀ Sm is not Cohen-Macaulay over Z Z/2Z Z, but it is Cohen-...

We construct for each n an Eulerian partially ordered set Tn of rank n + 1 whose ce-index provides a non-commutative generalization of the n-th Tchebyshev polynomial. We show that the order complex of each Tn is shellable, homeomorphic to a sphere, and that its face numbers minimize the expression max|x|≤1 ∣∣∣∑nj=0(fj−1/fn−1) · 2−j · (x− 1)j∣∣∣ among the f -vectors of all (n − 1)-dimensional si...