Enumeration of super-strong Wilf equivalence classes of permutations in the generalized factor order

Super-strong Wilf equivalence classes of the symmetric group ${\mathcal S}_n$ on $n$ letters, with respect to the generalized factor order, were shown by Hadjiloucas, Michos and Savvidou (2018) to be in bijection with pyramidal sequences of consecutive differences. In this article we enumerate the latter by giving recursive formulae in terms of a two-dimensional analogue of non-interval permutations. As a by-product, we obtain a recursively defined set of representatives of super-strong Wilf equivalence classes in ${\mathcal S}_n$. We also provide a connection between super-strong Wilf equivalence and the geometric notion of shift equivalence---originally defined by Fidler, Glasscock, Miceli, Pantone, and Xu (2018) for words---by showing that an alternate way to characterize super-strong Wilf equivalence for permutations is by keeping only rigid shifts in the definition of shift equivalence. This allows us to fully describe shift equivalence classes for permutations of size $n$ and enumerate them, answering the corresponding problem posed by Fidler, Glasscock, Miceli, Pantone, and Xu (2018).Comment: 18 pages, 5 table

INTERTWINED AND INCOMPATIBLE IDENTITIES IN THE ARGUMENTATION AGAINST THE INSTITUTIONALIZATION OF SAME SEX COUPLES’ COHABITATION AGREEMENT: "GREEK-ORTHODOXY" AND HOMOSEXUALITY

This research focuses on the ways in which "Greek-Orthodox" social identity is constructed and used as an argumentative resource against the institutionalization of same-sex couples’ cohabitation agreement. The analytic material consisted of comments put forward in the context of a public online deliberation on this issue held in Greece in 2015. Analysis, which used the principles of critical discursive psychology and rhetoric, highlights the construction of a solid "Greek-Orthodox" identity in which the concepts of "nation" and "religion" presuppose each other while at the same time they establish heteronormativity. Moreover, homosexuality is constructed as a “sin” that is incompatible with the "Greek-Orthodox" identity while the legal protection of same-sex relationships is represented as a threat to the Greek nation. These constructions are orientated to manage social accountability concerns of the commentators, while at the same time they potentially contribute to the preservation of hierarchical structures and power relations aiming to undermine LGBTQI+ claims.     Key words: Cohabitation agreement, Identities, Same-sex couple

Computing the average parallelism in trace monoids

Le lien vers arXiv : arXiv:cs/0112012v2The height of a trace is the height of the corresponding heap of pieces in Viennot's representation, or equivalently the number of factors in its Cartier-Foata decomposition. Let h(t) and |t| stand respectively for the height and the length of a trace t. Roughly speaking, |t| is the `sequential' execution time and h(t) is the `parallel' execution time. We prove that the bivariate commutative series \sum_t x^{h(t)}y^{|t|} is rational, and we give a finite representation of it. We use the rationality to obtain precise information on the asymptotics of the number of traces of a given height or length. Then, we study the average height of a trace for various probability distributions on traces. For the uniform probability distribution on traces of the same length (resp. of the same height), the asymptotic average height (resp. length) exists and is an algebraic number. To illustrate our results and methods, we consider a couple of examples: the free commutative monoid and the trace monoid whose independence graph is the ladder graph

Primary Total Knee Arthroplasty in Valgus Deformity

Proper limb and component alignments as well as soft tissue balance are vital for the longevity and optimal long-term outcomes of total knee arthroplasty (TKA). The majority of orthopedic surgeons agree that the total arthroplasty procedure in valgus knees with a deformity of more than 10° is technically demanding and may prove challenging. At the time of operation, the bone and soft tissue abnormalities that should be corrected make accurate axis restoration, correct component positioning and joint stability attaining a difficult task. Specific pathologic anatomic changes associated with valgus knee should be understood preoperatively and estimated so as to select the proper surgical method, to enhance component position and to restore soft-tissue balancing. The purpose of this chapter is to consider all the valgus knee anatomical variations, to analyze the best preoperative planning and to evaluate the type of implant, constrained or not. Lastly, it will also be underlying the current main approaches and techniques to be proposed in the literature for both bone cuts and soft tissue management of valgus knees and if minimally invasive techniques can be performed in severe deformed knees

On the support of the free Lie algebra: the Schutzenberger problems

Combinatoric

On super-strong Wilf equivalence classes of permutations

Super-strong Wilf equivalence is a type of Wilf equivalence on words that was originally introduced as strong Wilf equivalence by Kitaev et al. [Electron. J. Combin. 16(2)] in 2009. We provide a necessary and sufficient condition for two permutations in n letters to be super-strongly Wilf equivalent, using distances between letters within a permutation. Furthermore, we give a characterization of such equivalence classes via two-colored binary trees. This allows us to prove, in the case of super-strong Wilf equivalence, the conjecture stated in the same article by Kitaev et al. that the cardinality of each Wilf equivalence class is a power of 2