A Tutte polynomial for partially ordered sets
type: Item
instance of: scholarly article
title: A Tutte polynomial for partially ordered sets
zbMATH Open document ID: 0793.05039
author: Gary Gordon
published in: Journal of Combinatorial Theory. Series B
publication date: 1994-08-10T00:00:00Z
review text: We investigate the Tutte polynomial of a greedoid associated to a partially ordered set. In this case, we explore the deletion-contraction formula in two ways and develop an antichain expansion for the polynomial. We show that the polynomial can determine the number of order ideals, order filters and antichains of all sizes of a poset \(P\), but neither the number of chains, multichains, extensions, nor the dimension of \(P\). We show how to compute the polynomial for the direct sum, ordinal sum and ordinal product of two posets, but show this cannot be done for the direct product. We also show it is possible to determine \(f(P^*)\) from \(f(P)\), where \(P^*\) is the dual poset of \(P\). We also consider the idea of feasible isomorphism of two greedoids and show that two feasibly isomorphic greedoids have the same polynomial.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 06A07
zbMATH DE Number: 562389
zbMATH Keywords: antimatroid
zbMATH Keywords: Tutte polynomial
zbMATH Keywords: greedoid
zbMATH Keywords: partially ordered set
zbMATH Keywords: deletion- contraction formula
zbMATH Keywords: antichain expansion
zbMATH Keywords: feasible isomorphism
MaRDI profile type: Publication
OpenAlex ID: W2033842749
DOI: 10.1006/JCTB.1993.1060
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description: scientific article; zbMATH DE number 562389