Add to ORKGGiven a naturally labelled graded poset P with r ranks, the alternating sum W (P, −1): = � (−1) des(w) w∈L(P) is related to a quantity occurring in the Charney-Davis Conjecture on flag simplicial spheres. When |P | − r is odd it vanishes. When |P | − r is even and P satisfies the Neggers-Stanley Conjecture, it has sign (−1) |P |−r 2. We interpret this quantity combinatorially for several classes of graded posets P, including certain disjoint unions of chains and products of chains. These interpretations involve alternating multiset permutations, Baxter permutations, Catalan numbers, and Franel numbers
Abstract. We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyr...
Let $\mathcal{P}$ be a simple thin polyomino and $\Bbbk$ a field. Let $R$ be the toric $\Bbbk$-algeb...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
We generalize the notion of graded posets to what we call sign-graded (labeled) posets. We prove tha...
Abstract. For a graded naturally labelled poset P, it is shown that the P-Eulerian polynomial W(P, t...
Abstract. We investigate various bases for the °ag f-vectors of Eulerian posets. Many of the change-...
AbstractFor a graded naturally labelled poset P, it is shown that the P-Eulerian polynomialW(P,t):=∑...
AbstractA permutation is called parity alternating if its entries assume even and odd integers alter...
University of Minnesota Ph.D. dissertation. December 2008. Major: Mathematics. Advisor: Dennis Stant...
AbstractAlternating sign matrices (ASMs) are square matrices with entries 0, 1, or −1 whose rows and...
We prove results in arithmetic combinatorics involving sums of prime numbers and also some variants ...
We study flag enumeration in intervals in the Bruhat order on a Coxeter group by means of a structur...
We give a convolution formula for cd-index coefficients. The convolution formula, together with the ...
AbstractSuppose a finite poset P is partitioned into three non-empty chains so that, whenever p, q∈P...
AbstractLet the sign of a standard Young tableau be the sign of the permutation you get by reading i...
Abstract. We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyr...
Let $\mathcal{P}$ be a simple thin polyomino and $\Bbbk$ a field. Let $R$ be the toric $\Bbbk$-algeb...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...
We generalize the notion of graded posets to what we call sign-graded (labeled) posets. We prove tha...
Abstract. For a graded naturally labelled poset P, it is shown that the P-Eulerian polynomial W(P, t...
Abstract. We investigate various bases for the °ag f-vectors of Eulerian posets. Many of the change-...
AbstractFor a graded naturally labelled poset P, it is shown that the P-Eulerian polynomialW(P,t):=∑...
AbstractA permutation is called parity alternating if its entries assume even and odd integers alter...
University of Minnesota Ph.D. dissertation. December 2008. Major: Mathematics. Advisor: Dennis Stant...
AbstractAlternating sign matrices (ASMs) are square matrices with entries 0, 1, or −1 whose rows and...
We prove results in arithmetic combinatorics involving sums of prime numbers and also some variants ...
We study flag enumeration in intervals in the Bruhat order on a Coxeter group by means of a structur...
We give a convolution formula for cd-index coefficients. The convolution formula, together with the ...
AbstractSuppose a finite poset P is partitioned into three non-empty chains so that, whenever p, q∈P...
AbstractLet the sign of a standard Young tableau be the sign of the permutation you get by reading i...
Abstract. We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyr...
Let $\mathcal{P}$ be a simple thin polyomino and $\Bbbk$ a field. Let $R$ be the toric $\Bbbk$-algeb...
36 pages, 22 figuresWe introduce a family of domino tilings that includes tilings of the Aztec diamo...