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Let T be a tree on n vertices and let L q T be the q-analogue of its Laplacian. For a partition λ ⊢ n , let the normalized immanant of L q T indexed by λ be denoted as I m m ¯ λ ( L q T). A string of inequalities among I m m ¯ λ ( L q T) is known when λ varies over hook partitions of n as the size of the first part of λ decreases. In this work, we show a similar sequence of inequalities when λ varies over two row partitions of n as the size of the first part of λ decreases. Our main lemma is an identity involving binomial coefficients and irreducible character values of S n indexed by two row partitions. Our proof can be interpreted using the combinatorics of Riordan paths and our main lemma admits a nice probabilisitic interpretation involving peaks at odd heights in generalized Dyck paths or equivalently involving special descents in Standard Young Tableaux with two rows. As a corollary, we also get inequalities between I m m ¯ λ 1 ( L q T 1 ) and I m m ¯ λ 2 ( L q T 2 ) when T 1 and T 2 are comparable trees in the G T S n poset and when λ 1 and λ 2 are both two rowed partitions of n, with λ 1 having a larger first part than λ 2 . [ABSTRACT FROM AUTHOR]

Background: Knowledge on distribution and burden of diseases in a community is essential for planning of public health services. In the absence of information on morbidity profile through community-based surveys, facility-based data provide a good alternative. The aim of this study was to describe the morbidity profile of patients attending the Centre for Urban Health All India Institute of Medical Sciences (AIIMS) Bhopal (CUHA)., Methodology: A record-based descriptive study was carried out in the CUHA Bhopal, Madhya Pradesh, Central India. Information on age, gender, residence, new case, and principal diagnosis were extracted from the outpatient registers for the period between January 2014 and December 2014. Only newly registered patients for the study year (2014) were included. Descriptive analysis was done., Results: A total of 6685 new episodes of illnesses were treated. Adults (>15 years) constituted about 85.0%. Overall, the respiratory disorders were the most common (27.2%) followed by the digestive disorders (10.9%), circulatory disorders (9.9%), musculoskeletal disorders (8.8%), and infectious and parasitic disorders (7.4%)., Conclusion: This study gives a brief description of the morbidity profile of patients attending a primary health care center over a period of 1 year. This knowledge would help in planning health services to meet the patients' needs and help in training health staff., Competing Interests: Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.