New q-analogs of Stirling numbers of the second kind(and the first kined) are derived from a poset on [2k] using Stanley’s P -partition theory [?]. We also generalize to the poset on the set [rk].

Stanley, R.P., Some applications of algebra to combinatorics, Discrete Applied Mathematics 34

Stanley Cohen [5] was born on 17 November 1922 in Brooklyn, New York. His father was a tailor and his mother a housewife who immigrated to the United States from Russia in the early 1900s. Cohen spent his early education in the New York City public school system, and attended the city college, Brooklyn College [9], for his undergraduate studies. Brooklyn College [9] had no tuition, which allowe...

Article history: Received 11 December 2006 Available online 16 April 2009

We introduce the notion of 321-avoiding permutations in the affine Weyl group W of type An−1 by considering the group as a George group (in the sense of Eriksson and Eriksson). This enables us to generalize a result of Billey, Jockusch and Stanley to show that the 321-avoiding permutations in W coincide with the set of fully commutative elements; in other words, any two reduced expressions for ...

In work culminating in Know How (2009), Jason Stanley argues, against Gilbert Ryle, that knowledge-how is a species of knowledge-that. In How Propaganda Works (2015), Stanley portrays this work as undermining a “flawed ideology” supporting elitist valuations of intellectual work and workers. However, the link between Stanley’s two philosophical projects is weak. Ryle’s distinction between knowl...

We prove that the number of cyclically symmetric, self-complementary plane partitions contained in a cube of side 2n equals the square of the number of totally symmetric, self-complementary plane partitions contained in the same cube, without explicitly evaluating either of these numbers. This appears to be the first direct proof of this fact. The problem of finding such a proof was suggested b...