signed ordinances are a major part of religious ordinances having existed as normative before the institution of divine canonization and having been approved without any or with slight modification by the legislator and having entered the canon law. some neo-mu‘tazilites believe these ordinances are related to the praxes of the time of legislation, and by the disappearance of those customs they...

We define a new object, called a signed poset, that bears the same relation to the hyperoctahedral group B n (i.e., signed permutations on n letters), as do posets to the symmetric group S n. We then prove hyperoctahedral analogues of the following results: (1) the generating function results from the theory of P-partitions; (2) the fundamental theorem of finite distributive lattices (or Birkho...

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The problem of reconstructing signed permutations on n elements from their erroneous patterns distorted by reversal errors is considered in this paper.A reversal is the operation of taking a segment of the signed permutation, reversing it, and flipping the signs of its elements. The reversal metric is defined as the least number of reversals transforming one signed permutation into another. It ...

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t(x · 1 + 0 · s) = t · x = 0. Therefore f ′ is injective. Now we need to show that im f ′ = ker g′. We have g′(f ′(x/s)) = g(f(x)/s) = (g ◦ f)(x)/s = 0, so im f ′ ⊂ ker g′. Conversely, if g′(y/s) = 0, then g(y)/s = 0, so there exists t ∈ S so that t · g(y) = g(t · y) = 0. Therefore t · y ∈ ker g, so t · y ∈ im f . Let x ∈ X so that f(x) = t · y. Then f ′(x/(st)) = f(x)/(st) = (t · y)/(st) = y/s...

This paper shows that the number of sign patterns of totally non-zero symmetric n-by-n matrices, up to conjugation by monomial matrices and negation, is equal to the number of unlabelled graphs on n vertices.

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We analyze the most commonly used method for shuffling cards. The main result is a simple expression for the chance of any arrangement after any number of shuffles. This is used to give sharp bounds on the approach to randomness: $ log, n + 0 shuffles are necessary and sufficient to mix up n cards. Key ingredients are the analysis of a card trick and the determination of the idempotents of a na...