A long-standing conjecture of Stanley states that every Cohen– Macaulay simplicial complex is partitionable. We disprove the conjecture by constructing an explicit counterexample. Due to a result of Herzog, Jahan and Yassemi, our construction also disproves the conjecture that the Stanley depth of a monomial ideal is always at least its depth.

We have introduced the Janet's algorithm for the Stanley decomposition of a monomial ideal I ⊂ S = K[x 1 , ..., x n ] and prove that Janet's algorithm gives the squarefree Stanley decomposition of S/I for a squarefree monomial ideal I. We have also shown that the Janet's algorithm gives a partition of a simplicial complex.

1875-9521/$ see front matter 2014 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.entcom.2013.06.003 q This paper has been recommended for acceptance by Junia Anacleto, PhD on Physics. ⇑ Corresponding author. Tel.: +1 306 966 4886. E-mail addresses: [email protected] (A. Tavassolian), kevin.stanley@ usask.ca (K.G. Stanley), [email protected] (C. Gutwin). Amin Tavassolian ⇑, Ke...

We study the class C of symmetric functions whose coefficients in the Schur basis can be described by generating functions for sets of tableaux with fixed shape. Included in this class are the Hall-Littlewood polynomials, k-Schur functions, and Stanley symmetric functions; functions whose Schur coefficients encode combinatorial, representation theoretic and geometric information. While Schur fu...

Intellectualism about knowledge-how is the view that, in short, an agent’s knowing how to φ is grounded that agent’s propositional attitudes vis-à-vis φ-ing. Themost popular andwell-developed contemporary strategy for defending this position appeals, in the main, to linguistic considerations (e.g. Stanley &Williamson 2001; Stanley 2011), and consequently, the plausibility of intellectualism in ...