Bar code for monomial ideals

2017/01/07 by Ceria, Michela · 2 citations
#05E40 #13P10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.01781

Abstract

Aim of this paper is to count 0-dimensional stable and strongly stable ideals in 2 and 3 variables, given their (constant) affine Hilbert polynomial. To do so, we define the Bar Code, a bidimensional structure representing any finite set of terms M and allowing to desume many properties of the corresponding monomial ideal I, if M is an order ideal. Then, we use it to give a connection between (strongly) stable monomial ideals and integer partitions, thus allowing to count them via known determinantal formulas.

Cited by

• Enumerating finite O-sequences: sub-Fibonacci behavior and growth estimates
• Counting finite O-sequences of a given multiplicity

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