Multiplicity of the trivial representation in rank-selected homology of the partition lattice

We study the multiplicity $b_S(n)$ of the trivial representation in the symmetric group representations $\beta_S$ on the (top) homology of the rank-selected partition lattice $\Pi_n^S$. We break the possible rank sets $S$ into three cases: (1) $1\not\in S$, (2) $S=1,..., i$ for $i\ge 1$ and (3) $S=1,..., i,j_1,..., j_l$ for $i,l\ge 1$, $j_1 > i+1$. It was previously shown by Hanlon that $b_S(n)=0$ for $S=1,..., i$. We use a partitioning for $\Delta(\Pi_n)/S_n$ due to Hersh to confirm a conjecture of Sundaram that $b_S(n)>0$ for $1\not\in S$. On the other hand, we use the spectral sequence of a filtered complex to show $b_S(n)=0$ for $S=1,..., i,j_1,..., j_l$ unless a certain type of chain of support $S$ exists. The partitioning for $\Delta(\Pi_n)/S_n$ allows us then to show that a large class of rank sets $S=1,..., i,j_1,..., j_l$ for which such a chain exists do satisfy $b_S(n)>0$. We also generalize the partitioning for $\Delta(\Pi_n)/S_n$ to $\Delta(\Pi_n)/S_{\lambda}$; when $\lambda = (n-1,1)$, this partitioning leads to a proof of a conjecture of Sundaram about $S_1\times S_{n-1}$-representations on the homology of the partition lattice

An exploration of groups dynamics and the impact of unconscious processes

Despite extensive research on groups, organisations continue to experience problems with them. Is this an inherent feature of the nature of groups? This article aims to provide a practical understanding of the unconscious processes in groups and how these impact on group functioning. It further elaborates some guidelines for managers on optimising team / group performance. The article interrogates the work of Sigmund Freud regarding his views on how groups function, drawing mainly on his work Group Psychology and Analysis of the Ego (1921). It asks if a study of Freud’s work can help organisations reconsider the nature of groups, their potential inherent problems, and understanding the challenges to improving how groups function

Do we face a third revolution in human history? If so, how will public health respond?

<b>Background:</b> A range of evidence suggests that the dominant culture associated with the economic systems of ‘modern’ societies has become a major source of pressure on global resources and may precipitate a third revolution in human history, with major implications for health and well-being. <b>Objective:</b> This paper aims to consider whether there are historical analogies with contemporary circumstances which might help us make connections between past and present predicaments in the human condition; to highlight the underpinnings of such predicaments in the politico-economic and cultural systems found in ‘modern’ societies; to outline questions prompted by this analysis, and stimulate greater debate around the issues raised. <b>Methods:</b> We draw on evidence and arguments condensed from complex research and theorizing from multiple disciplines. <b>Results:</b> Contemporary evidence suggests that global depletion of a key energy resource (oil), increasing environmental degradation and imminent climate change can be linked to human socio-economic and cultural systems which are now out of balance with their environment. Those systems are associated with Western-type societies, where political philosophies of neo-liberalism, together with cultural values of individualism, materialism and consumerism, support an increasingly globalized capitalist economic system. Evidence points to a decline of psychological and social well-being in such societies. <b>Conclusion:</b> We need to work out how to prevent/ameliorate the harms likely to flow from climate change and rising oil costs. Public health professionals face the challenge of preventing adverse health consequences likely to result from continued adherence to the have-it-all mindset prevailing in contemporary Western societies. Equally, we need to seek out the potential health dividends that could be realized in terms of reduced obesity, improved well-being and greater social equity, while not under-estimating the likelihood of profound resistance, from many sectors of society, to unwanted but inevitable change

An Investigation Into the Stickiness of Tacit Knowledge Transfer

Managing knowledge is of central importance to organisational success (Chia, 2003). The focus of knowledge management systems has progressed from the management of explicit knowledge to management of tacit knowledge. The importance of tacit knowledge is highlighted by Wah (1999:27) who argues that 90% of the knowledge in any organisation is embedded and synthesised in people’s minds. However, tacit knowledge is the specific type of knowledge that is characterised as extremely difficult to capture or to articulate (Nonaka, 1994). Academics and practitioners alike have gained an appreciation for this type of knowledge. Tacit knowledge has become recognised as a significant and advantageous part of the knowledge base of both individuals and organisations. However, in order for organisations to take full advantage of their current tacit knowledge base they must encourage individuals to both capture and transfer it. This article addresses the difficulties associated with the capture and transfer of tacit knowledge. Szulanski (2000) identified a concept he called ‘stickiness’ to describe the difficulty of this process. It is generally assumed that tacit knowledge is both costly and time-consuming to transfer (Szulanski, 1995). It has been shown however, that tacit knowledge is transferred on a regular basis within organisations, sometimes with great difficulty and sometimes with ease. In order to assist both individuals and organisations in their attempt to transfer tacit knowledge we must first identify the obstacles that stand in their way. Szulanski (2000) discussed eight areas of difficulty which are experienced during a knowledge transfer. He categorises them into two separate areas of the transfer, namely, knowledge characteristics and situational characteristics, with four difficulties identified within each. This paper uses these eight areas of difficulty as the bounds within which to test the ‘stickiness’ of tacit knowledge transfer. The authors conducted a systematic empirical investigation into the ‘stickiness’ of tacit knowledge transfer through qualitative semi-structured interviews and an in-depth literature review. The semi-structured interviews consisted of a detailed examination of tacit knowledge transfers among IT support professionals and both integration and software engineers. The interviewees were asked to discuss in detail times when they were involved in a transfer of tacit knowledge, and were then probed for further information on the difficulties they experienced and the obstacles they encountered. Analysis of the interview transcripts showed a vast difference in the spread and significance of difficulties experienced during the transfer of tacit knowledge compared to that of knowledge in general. However, it is important to note that Szulanski’s eight areas of difficulty are a sufficient basis upon which to study tacit knowledge transfer. Three areas of difference stood out, firstly the influence of the source on the transfer of tacit knowledge is significantly stronger than that of knowledge in general, secondly the reasons for transferring incomplete knowledge varied greatly from that discussed by Szulanski, and finally the effect of organisation and industry culture on the likelihood of tacit knowledge transfer is considerably higher. Being aware of the difficulties that emerge during a tacit knowledge transfer allows those engaging in it to reduce these difficulties and to seek solutions to them

A Note on the Homology of Signed Posets

Let S be a signed poset in the sense of Reiner [4]. Fischer [2] defines the homology of S , in terms of a partial ordering P ( S ) associated to S , to be the homology of a certain subcomplex of the chain complex of P ( S ). In this paper we show that if P ( S ) is Cohen-Macaulay and S has rank n , then the homology of S vanishes for degrees outside the interval [ n /2, n ].Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46242/1/10801_2005_Article_415337.pd

Jack symmetric functions and some combinatorial properties of young symmetrizers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27452/1/0000492.pd

A Markov chain on the symmetric group and Jack symmetric functions

Diaconis and Shahshahani studied a Markov chain W[function of (italic small f)](1) whose states are the elements of the symmetric group S[function of (italic small f)]. In W[function of (italic small f)](1), you move from a permutation [pi] to any permutation of the form [pi](i, j) with equal probability. In this paper we study a deformation W[function of (italic small f)]([alpha]) of this Markov chain which is obtained by applying the Metropolis algorithm to W[function of (italic small f)](1). The stable distribution of W[function of (italic small f)]([alpha]) is [alpha][function of (italic small f)]-c([pi]) where c([pi]) denotes the number of cycles of [pi]. Our main result is that the eigenvectors of the transition matrix of W[function of (italic small f)]([alpha]) are the Jack symmetric functions. We use facts about the Jack symmetric functions due to Macdonald and Stanley to obtain precise estimates for the rate of convergence of W[function of (italic small f)]([alpha]) to its stable distribution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30109/1/0000481.pd

The fixed-point partition lattices

Let σ be a permutation of the set {1,2, ..., n} and let [Pi](N) denote the lattice of partitions of {1,2, ..., n}. There is an obvious induced action of σ on [Pi](N); let [Pi](N)σ = L denote the lattice of partitions fixed by σ