We relate the parity of the partition function to the parity of the q-series coefficients of certain powers of the modular discriminant using their generating functions. This allows us to make statements about the parity of the initial values of the partition function as well as obtain a modified Euler recurrence for its parity.

IMPORTANCE The passage of the 2008 Mental Health Parity and Addiction Equity Act and the 2010 Affordable Care Act incorporated parity for substance use disorder (SUD) treatment into federal legislation. However, prior research provides us with scant evidence as to whether federal parity legislation will hold the potential for improving access to SUD treatment. OBJECTIVE To examine the effect ...

Our objectives were 1) to compare reproductive performance across parity and lifetime performance in sow groups categorized by the number of pigs born alive (PBA) in parity 1 and 2) to examine the factors associated with more PBA in parity 1. We analyzed 476,816 parity records and 109,373 lifetime records of sows entered into 125 herds from 2008 to 2010. Sows were categorized into 4 groups base...

Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resource-constrained omega-regular specifications, energy ...

Deliberate injection of faults into cryptographic devices is an effective cryptanalysis technique against symmetric and asymmetric encryption algorithms. In this paper we will describe parity code based concurrent error detection (CED) approach against such attacks in substitution-permutation network (SPN) symmetric block ciphers [22]. The basic idea compares a carefully modified parity of the ...

BACKGROUND Adverse pregnancy outcome is an important public health problem that has been partly associated with increasing maternal parity. AIM To determine the effect of parity on maternal body mass index (BMI), mineral element status and newborn anthropometrics. METHODS Data for 349 pregnant women previously studied for the impacts of maternal plasma mineral element status on pregnancy an...

This paper presents a theorem concerning a matroid with the parity condition. The theorem provides matroid generalizations of graph-theoretic results of Lewin [3] and Gallai [1]. Let M=(E, F) be a matroid, where E is a finite set of elements and F is the family of independent sets of M (in this paper, we presuppose a knowledge of matroid theory; our standard reference is Welsh [4]). Assume that...

According to models estimated separately for second-, third-, and fourth-birth rates in Norway, an increase took place from the mid-1970s to about 1990, given age and duration since last previous birth. A similar rise in the birth rates was seen in Sweden, except that the upturn at short durations was sharper. It is shown in this study, using Norwegian register data, that the increase partly re...

We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermions in vector-like — but otherwise generic — representations of the gauge group. QCD, supersymmetric Yang–Mills theory, and orientifold field theories, all belong to this class. We argue that charge conjugation is not spontaneously broken as long as Lorentz invariance is maintained. Uniqueness of th...

Following the book [9] by Dunkl and Xu and the paper [23] by Xu we will assume that αj ≥ 0 for each j = 0, 1, . . . , k although one would expect that the range of validity can be extended analytically to the domain αj > −12 for each j. We will also exclude the case k = 1, α0 = α1 = 0 because we want the constant μ defined below in (1.5) to be positive. The parity vector p = (p0, p1, . . . , pk...