title: Lower bounds on the sizes of defining sets in full n-Latin squares and full designs

authors: Cavenagh, Nicholas J.

subjects: Science & Technology

abstract: The full n-Latin square is the n×n array with symbols 1, 2, . . . , n in each cell. In this paper we show, as part of a more general result,that any defining set for the full n-Latin square has size n³(1 − o(1)). The full design N(v, k) is the unique simple design with parameters (v,k,{v-2 \atopwithdelims ()k-2}); that is, the design consisting of all subsets of size k from a set of size v. We show that any defining set for the full design N(v, k) has size {v\atopwithdelims ()k}(1-o(1)) (as v-k becomes large). These results improve existing results and are asymptotically optimal. In particular, the latter result solves an open problem given in (Donovan, Lefevre, et al, 2009), in which it is conjectured that the proportion of blocks in the complement of a full design will asymptotically approach zero.

text: Lower bounds on the sizes of defining sets in full n-Latin squares and full designs The full n-Latin square is the n×n array with symbols 1, 2, . . . , n in each cell. In this paper we show, as part of a more general result,that any defining set for the full n-Latin square has size n³(1 − o(1)). The full design N(v, k) is the unique simple design with parameters (v,k,{v-2 \atopwithdelims ()k-2}); that is, the design consisting of all subsets of size k from a set of size v. We show that any defining set for the full design N(v, k) has size {v\atopwithdelims ()k}(1-o(1)) (as v-k becomes large). These results improve existing results and are asymptotically optimal. In particular, the latter result solves an open problem given in (Donovan, Lefevre, et al, 2009), in which it is conjectured that the proportion of blocks in the complement of a full design will asymptotically approach zero.

year: 2018

title: Alternative Communities in Aotearoa, New Zealand: The Cohousing Lifestyle

authors: Dod, Abha

subjects: community

abstract: In this research, I aimed to explore the benefits and challenges of living in a cohousing community, as a form of intentional community. I also aimed to investigate the impact of intentional design on the experience of living within the cohousing model of community. Information was gathered from fourteen residents of Earthsong Eco-Neighbourhood, both current and past, via interviews. The analysis revealed that the lifestyle within cohousing communities produced a positive experience of collective living, accompanied by specific benefits and challenges, as expressed by residents of Earthsong. The primary benefits of living in cohousing included social connection/support, shared facilities and responsibilities, and environmental design. The associated challenges included the management of interpersonal relationships, community decision-making, and practicality of design features. The unique design of cohousing influenced social, economic, and environmental aspects of day to day living. This impacted the experience of living in cohousing as residents consciously engaged in sustainable living practices. In support of theoretical explanations of intentional community, residents of Earthsong expressed positive experiences of living in cohousing. They believed that the environment was supportive, cooperative, and enjoyable. The community design was seen to impact the experience of cohousing as the focus placed on social connections allowed for the sharing of support and resources. In turn, a safe and cohesive neighbourhood made day to day life easier and enjoyable for residents of Earthsong. This study highlighted the social, economic, and environmental benefits and challenges of intentional community design.

text: Alternative Communities in Aotearoa, New Zealand: The Cohousing Lifestyle In this research, I aimed to explore the benefits and challenges of living in a cohousing community, as a form of intentional community. I also aimed to investigate the impact of intentional design on the experience of living within the cohousing model of community. Information was gathered from fourteen residents of Earthsong Eco-Neighbourhood, both current and past, via interviews. The analysis revealed that the lifestyle within cohousing communities produced a positive experience of collective living, accompanied by specific benefits and challenges, as expressed by residents of Earthsong. The primary benefits of living in cohousing included social connection/support, shared facilities and responsibilities, and environmental design. The associated challenges included the management of interpersonal relationships, community decision-making, and practicality of design features. The unique design of cohousing influenced social, economic, and environmental aspects of day to day living. This impacted the experience of living in cohousing as residents consciously engaged in sustainable living practices. In support of theoretical explanations of intentional community, residents of Earthsong expressed positive experiences of living in cohousing. They believed that the environment was supportive, cooperative, and enjoyable. The community design was seen to impact the experience of cohousing as the focus placed on social connections allowed for the sharing of support and resources. In turn, a safe and cohesive neighbourhood made day to day life easier and enjoyable for residents of Earthsong. This study highlighted the social, economic, and environmental benefits and challenges of intentional community design.

year: 2013

title: Approaching Māori language through meaning: The predominance of Indo-European models of relationships within propositions

authors: Whaanga, Hēmi

subjects: Te reo Māori

abstract: In every language, there are relationships between predicators (such as, for example, 'go'/'haere') and arguments (such as, for example, ‘James'/'Hēmi’). One such relationship that has been proposed is that of agency. Thus, in 'James goes'/ ‘E haere ana a Hēmi’), 'James'/'Hēmi' can be said to be the agent of the action 'go'/'haere'. Much of the international literature on relationships of this type is based on research on English and it has been claimed that the relationships that have been identified are universals. However, there may be differences among languages, differences that are attributable to the fact that different languages encode different ways of perceiving divisions in perceptual space. My aim here is to demonstrate, with reference to a number of different models of predicator/ argument relations, that most of them are based on assumptions that derive from the structure of Indo-European languages, English in particular. In Part 2 of this paper (to appear in a subsequent issue of this Journal), the implications of this discussion will be examined with reference to an analysis of Māori in terms of relationships within propositions.

text: Approaching Māori language through meaning: The predominance of Indo-European models of relationships within propositions In every language, there are relationships between predicators (such as, for example, 'go'/'haere') and arguments (such as, for example, ‘James'/'Hēmi’). One such relationship that has been proposed is that of agency. Thus, in 'James goes'/ ‘E haere ana a Hēmi’), 'James'/'Hēmi' can be said to be the agent of the action 'go'/'haere'. Much of the international literature on relationships of this type is based on research on English and it has been claimed that the relationships that have been identified are universals. However, there may be differences among languages, differences that are attributable to the fact that different languages encode different ways of perceiving divisions in perceptual space. My aim here is to demonstrate, with reference to a number of different models of predicator/ argument relations, that most of them are based on assumptions that derive from the structure of Indo-European languages, English in particular. In Part 2 of this paper (to appear in a subsequent issue of this Journal), the implications of this discussion will be examined with reference to an analysis of Māori in terms of relationships within propositions.

year: 2001-09