Let r(w) denote the number of reduced words for an element w in a Coxeter group w. Stanley proved a formula for r(w) when W is the symmetric group A,,, and he suggested looking at r(w) for the ffie group Aln. We prove that for any afline Coxeter group R, there is a finite number of types of elements in xX, such that to every element w can be associated (I) a type t, (2) an element u in the &rit...

We prove that the number of partitions of an integer into at most b distinct parts of size at most n forms a unimodal sequence for n sufficiently large with respect to b. This resolves a recent conjecture of Stanley and Zanello.

In his chapter “Performative and Passionate Utterance” which appears in Philosophy The Day After Tomorrow, Stanley Cavell makes a claim for what he describes as the expressive or passional aspects of speech. This claim (plea might be a more appropriate term) is, in part, a response to what Cavell regards as a missed opportunity or failing in Austin’s theory of the performative utterance, an opp...

We prove a recent conjecture of B. Berndt and B. Kim regarding the positivity of the coefficients in the asymptotic expansion of a class of partial theta functions. This generalizes results found in Ramanujan’s second notebook and recent work of Galway and Stanley.

Another question of pubiie interest has presented itself for discussion. Stanley W. Turner, Auditor General, has been drawing salary at the rate of $3,000 per year, since May 27, 1893. There is now a very serious question as to the validity of the law granting him that salary, and it is not impossible that he may have to return to the state several hundred dollars illegally drawn. The legislatu...

The Gaia hypothesis [Lovelock, J., Margulis, L., 1974. Atmospheric homeostasis: the Gaia hypothesis. Tellus 26, 1], that the earth functions as a self-regulating system, has never sat particularly comfortably with ideas in mainstream biology [Anon, 2002. In pursuit of arrogant simplicities. Nature 416, 247]. A lack of any clear role for evolution in the model has led to claims of teleology-that...

This article explores the history of the two results in integer partitions known as Stanley’s theorem and Elder’s theorem. While history has credited Richard Stanley with the discovery of the results, we note that Nathan Fine had established these results among a host of other partition identities over a decade earlier. In tribute to Fine, analogues in the sets of odd partitions and distinct pa...

We show that Stanley’s Conjecture holds for square free monomial ideals in five variables, that is the Stanley depth of a square free monomial ideal in five variables is greater or equal with its depth.

We use an interesting result of probabilistic flavor concerning the product of two permutations consisting of one cycle each to find an explicit formula for the average number of block interchanges needed to sort a permutation of length n.