title: Complete sets of metamorphoses: Twofold 4-cycle systems into twofold 6-cycle systems

authors: Billington, Elizabeth J.

subjects: Cycle decomposition

abstract: Let (X,C) denote a twofold k-cycle system with an even number of cycles. If these k-cycles can be paired together so that: (i) each pair contains a common edge; (ii) removal of the repeated common edge from each pair leaves a (2k-2)-cycle; (iii) all the repeated edges, once removed, can be rearranged exactly into a collection of further (2k-2)-cycles; then this is a metamorphosis of a twofold k-cycle system into a twofold (2k-2)-cycle system. The existence of such metamorphoses has been dealt with for the case of 3-cycles (Gionfriddo and Lindner, 2003) [3] and 4-cycles (Yazc, 2005) [7]. If a twofold k-cycle system (X,C) of order n exists, which has not just one but has k different metamorphoses, from k different pairings of its cycles, into twofold (2k-2)-cycle systems, such that the collection of all removed double edges from all k metamorphoses precisely covers 2 Kn, we call this a complete set of twofold paired k-cycle metamorphoses into twofold (2k-2)-cycle systems. In this paper, we show that there exists a twofold 4-cycle system (X,C) of order n with a complete set of metamorphoses into twofold 6-cycle systems if and only if n≡0,1,9,16 (mod 24), n≠9.

text: Complete sets of metamorphoses: Twofold 4-cycle systems into twofold 6-cycle systems Let (X,C) denote a twofold k-cycle system with an even number of cycles. If these k-cycles can be paired together so that: (i) each pair contains a common edge; (ii) removal of the repeated common edge from each pair leaves a (2k-2)-cycle; (iii) all the repeated edges, once removed, can be rearranged exactly into a collection of further (2k-2)-cycles; then this is a metamorphosis of a twofold k-cycle system into a twofold (2k-2)-cycle system. The existence of such metamorphoses has been dealt with for the case of 3-cycles (Gionfriddo and Lindner, 2003) [3] and 4-cycles (Yazc, 2005) [7]. If a twofold k-cycle system (X,C) of order n exists, which has not just one but has k different metamorphoses, from k different pairings of its cycles, into twofold (2k-2)-cycle systems, such that the collection of all removed double edges from all k metamorphoses precisely covers 2 Kn, we call this a complete set of twofold paired k-cycle metamorphoses into twofold (2k-2)-cycle systems. In this paper, we show that there exists a twofold 4-cycle system (X,C) of order n with a complete set of metamorphoses into twofold 6-cycle systems if and only if n≡0,1,9,16 (mod 24), n≠9.

year: 2012

title: Pacific parental engagement and intergenerational storytelling in Aotearoa New Zealand

authors: Cunningham, Emma

abstract: In this article, we focus on how Pacific family support places success of individuals within a wider narrative of intergenerational family stories, contributing to successful futures for the participating Pacific youth and their families. Guided by Pacific research principles, we used interviews with families and adolescents to explore the role of family narratives, in ten Pacific families in Aotearoa New Zealand, which supported academic success for their children. Our data sources included conversations with youth, their families, and visual representations created by the youth to illustrate their perceptions of parental support. The findings highlighted the role of families’ stories in supporting their children’s education. Strong intergenerational expectations were expressed from the dual perspectives of parents and their children. The formative role of family stories within the youths’ experiences of success provides opportunity to acknowledge the relational foundations of intergenerational stories.

text: Pacific parental engagement and intergenerational storytelling in Aotearoa New Zealand In this article, we focus on how Pacific family support places success of individuals within a wider narrative of intergenerational family stories, contributing to successful futures for the participating Pacific youth and their families. Guided by Pacific research principles, we used interviews with families and adolescents to explore the role of family narratives, in ten Pacific families in Aotearoa New Zealand, which supported academic success for their children. Our data sources included conversations with youth, their families, and visual representations created by the youth to illustrate their perceptions of parental support. The findings highlighted the role of families’ stories in supporting their children’s education. Strong intergenerational expectations were expressed from the dual perspectives of parents and their children. The formative role of family stories within the youths’ experiences of success provides opportunity to acknowledge the relational foundations of intergenerational stories.

year: 2022

title: Renewal and resistance: Moko in contemporary New Zealand

authors: Nikora, Linda Waimarie

subjects: maori

abstract: Moko is still here, contrary to the widely held belief that the art and custom of moko-Maori skin adornment-had vanished from New Zealand communities. Over the last two decades an increasingly visible number of Maori have revived and renewed the practice, taking colour into their skin. As an indigenous people, re-taking moko confronts and refutes the myth of a 'dying race'. It calls on Maori to recommit to strong Maori identities, customs and traditions and challenges the viewer to re-examine their social representations of moko and moko wearers. This paper reports the resistance strategies of a group of 83 moko wearers. Strategies include (1) educating, representing and reconstructing; (2) invalidating and minimizing representations; (3) building and enhancing social networks; and (4) securing cultural identity and pride. They reflect the celebration of cultural resilience.

text: Renewal and resistance: Moko in contemporary New Zealand Moko is still here, contrary to the widely held belief that the art and custom of moko-Maori skin adornment-had vanished from New Zealand communities. Over the last two decades an increasingly visible number of Maori have revived and renewed the practice, taking colour into their skin. As an indigenous people, re-taking moko confronts and refutes the myth of a 'dying race'. It calls on Maori to recommit to strong Maori identities, customs and traditions and challenges the viewer to re-examine their social representations of moko and moko wearers. This paper reports the resistance strategies of a group of 83 moko wearers. Strategies include (1) educating, representing and reconstructing; (2) invalidating and minimizing representations; (3) building and enhancing social networks; and (4) securing cultural identity and pride. They reflect the celebration of cultural resilience.

year: 2007