Engineering topics

Keller, Mitchel T.

Publications and source records attributed to Keller, Mitchel T..

2 records

DOE OSTI2022

Dimension of Restricted Classes of Interval Orders

Rabinovitch showed in 1978 that the interval orders having a representation consisting of only closed unit intervals have order dimension at most 3. Herein, this article shows that the same dimension bound applies to two other classes of posets: those having a representation consisting of unit intervals (but with a mixture of open and closed intervals allowed) and those having a representation consisting of closed intervals with lengths in {0,1}.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Combinatorial Reductions for the Stanley Depth of I and S/I

We develop combinatorial tools to study the realtionship between the Stanley depth of a monomial ideal I and the Stanley depth of its compliment S/I. Using these results we prove that if S is a polynomial ring with at most 5 indeterminates and I is a square-free monomial ideal, then the Stanley depth of I is strictly larger than the Stanley depth of S/I. Using a computer search, we extend the strict inequality to the case of polynomial rings with at most 7 indeterminates. This partially answers questinos asked by Proescu and Qureshi as well as Herzog.

Keller, Mitchel T.↗