Ascent sequences and the binomial convolution of Catalan numbers

In this paper, we consider two sets of pattern-avoiding ascent sequences: those avoiding both 201 and 210 and those avoiding 0021. In each case we show that the number of such ascent sequences is given by the binomial convolution of the Catalan numbers. The result for $\{201, 210\}$-avoiders completes a family of results given by Baxter and the current author in a previous paper. The result for 0021-avoiders, together with previous work of Duncan, Steingr\'{i}msson, Mansour, and Shattuck, completes the Wilf classification of single patterns of length 4 for ascent sequences.Comment: Revised according to the referees' comments. The proof of Lemma 5 has been moved to an appendi

Counting interesting elections

We provide an elementary proof of a formula for the number of northeast lattice paths that lie in a certain region of the plane. Equivalently, this formula counts the lattice points inside the Pitman--Stanley polytope of an n-tuple.Comment: 7 pages, 1 figure; published versio

On Packing Densities of Set Partitions

We study packing densities for set partitions, which is a generalization of packing words. We use results from the literature about packing densities for permutations and words to provide packing densities for set partitions. These results give us most of the packing densities for partitions of the set $\{1,2,3\}$. In the final section we determine the packing density of the set partition $\{\{1,3\},\{2\}\}$.Comment: 12 pages, to appear in the Permutation Patterns edition of the Australasian Journal of Combinatoric

Pattern Avoidance in k-ary Heaps

In this paper, we consider pattern avoidance in k-ary heaps, where the permutation associated with the heap is found by recording the nodes as they are encountered in a breadth-first search. We enumerate heaps that avoid patterns of length 3 and collections of patterns of length 3, first with binary heaps and then more generally with k-ary heaps

Enumeration schemes for vincular patterns

We extend the notion of an enumeration scheme developed by Zeilberger and Vatter to the case of vincular patterns (also called “generalized patterns ” or “dashed patterns”). In particular we provide an algorithm which takes in as input a set B of vincular patterns and search parameters and returns a recurrence (called a “scheme”) to compute the number of permutations of length n avoiding B or confirmation that no such scheme exists within the search parameters. We also prove that if B contains only consecutive patterns and patterns of the form σ1σ2 · · · σt−1 σt, then such a scheme must exist and provide the relevant search parameters. The algorithms are implemented in Maple and we provide empirical data on the number of small pattern sets admitting schemes. We make several conjectures on Wilf-classification based on this data. We also outline how to refine schemes to compute the number of B-avoiding permutations of length n with k inversions.

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Nucleus Support for Family Health (NASF) as a component of mental health care: perspectives of professionals family health strategy

Os NÃcleos de Apoio à SaÃde da FamÃlia (NASF) tem como objetivo ampliar a abrangÃncia e o escopo das aÃÃes da atenÃÃo bÃsica no Sistema Ãnico de SaÃde (SUS) brasileiro. Em consonÃncia com as atuais mudanÃas no modelo de atenÃÃo à saÃde mental defendido pelo SUS e tendo em vista o aumento do nÃmero de casos relacionados à temÃtica, a proposta NASF elege a SaÃde Mental como uma das Ãreas estratÃgicas de atuaÃÃo do programa. Considerando a necessidade de acompanhar as experiÃncias em curso no cenÃrio nacional, a presente investigaÃÃo objetivou compreender, sob a perspectiva de uma equipe SaÃde da FamÃlia (SF), o lugar do NASF no cuidado em saÃde mental na atenÃÃo bÃsica do municÃpio de Fortaleza-CE. Trata-se de uma pesquisa orientada pelo enfoque qualitativo, alinhado à vertente crÃtico interpretativa, desenvolvida por meio de anÃlise documental, observaÃÃo livre e entrevistas semi estruturadas, em uma unidade de saÃde localizada na Regional III de Fortaleza-CE, englobando todos os trabalhadores de uma das equipes atuantes no serviÃo. A categorizaÃÃo do material empÃrico levou a trÃs temas centrais, a saber: A) CompreensÃes dos profissionais da equipe SF investigada acerca do fenÃmeno âSaÃde Mentalâ; B) O cuidado em âSaÃde Mentalâ no contexto da atenÃÃo bÃsica: a prÃxis no cotidiano do serviÃo pesquisado e C) O lugar do NASF no cuidado em âSaÃde Mentalâ na atenÃÃo bÃsica. Os resultados apontaram a predominÃncia de uma visÃo estigmatizada e estereotipada da pessoa com transtorno mental por parte da maioria dos entrevistados, bem como assinalou um processo ainda incipiente de experiÃncias em saÃde mental compartilhadas entre profissionais da equipe SF e equipe NASF. Dentre as aÃÃes atualmente em curso observamos pouca interaÃÃo entre os profissionais das referidas equipes, de modo a concluirmos que a reorganizaÃÃo da atenÃÃo à saÃde, a partir da implantaÃÃo do NASF, vem enfrentando dificuldades de diversas naturezas no cenÃrio investigado. Apesar disto, reconhece-se que o processo se encontra em andamento, sendo de grande relevÃncia para o fortalecimento das aÃÃes de saÃde mental do municÃpio a garantia da existÃncia de espaÃos coletivos de discussÃo, planejamento, pactuaÃÃo e avaliaÃÃo dos processos de trabalhos conjuntos, ampliando assim, a capacidade resolutiva das aÃÃes de saÃde sob responsabilidade da EstratÃgia SaÃde da FamÃlia (ESF).The Centers for Family Health Support (CFHS) aims to expand the breadth and the scope of the actions of primary care in the Unified Health System (UHS) in Brazil. Aligned with current changes in the model of mental health care advocated by (UHS) and considering the increasing number of cases related to the topic, the CFHS proposal elects Mental Health as one of the strategic areas of operation of the program. Considering the need to monitor ongoing experiments in the national scenario, this research aimed to understand from the perspective of a Family Health Team (FHT), the place of CFHS concerning the mental health care in primary care in Fortaleza-CE. This research is characterized for having a qualitative approach, aligned to the critical interpretive perspective. It was developed through documentary analysis, observation and semi structured interviews in a health care establishment located in the third region of Fortaleza, covering all staff in one of the in service teams. The categorization of empirical data led to three main themes which are: A) understanding of professionals in a FH team investigated about the phenomenon of "Mental Health"; B) The "Mental Health" care in the context of primary care: the everyday practice in the investigated service and C) The place of (CHFS) in terms of care concerning "Mental Health" in primary care. The results indicate the predominance of a stigmatized and stereotyped vision of the person with a mental disorder by the majority of the respondents. It also marked a process of incipient mental health experiences shared among the professionals of health as well as the staff on the team of FH and CFHS. Among the currently ongoing actions there was little interaction among practitioners of those teams, so we concluded that the reorganization of health care, based on the implementation of CFHS, is facing different kinds of difficulties in the scenario investigated. Nevertheless, it is recognized that the process is already occurring and it is of great importance to the strengthening of the mental health services of the city to guarantee the existence of collective spaces of discussion, planning, pact and evaluation of the process of team work, thus extending the resolution capability in health actions under the responsibility of the Family Health Strategy (FHS)