A square involution is a square permutation which is also an involution. In this paper we give the enumeration of square involutions, using purely combinatorial methods, by establishing a bijective correspondence with a class of lattice paths. As a corollary to our result, we enumerate various subclasses of square involutions, including the classes of triangular, decomposable, and fat involutions.

Breast cancer patients diagnosed within five years following pregnancy have increased metastasis and decreased survival. A hallmark of postpartum biology that may contribute to this poor prognosis is mammary gland involution, involving massive epithelial cell death and dramatic stromal remodeling. Previous studies show pro-tumorigenic properties of extracellular matrix (ECM) isolated from roden...

After puberty, the thymus undergoes a dramatic loss in volume, in weight and in the number of thymocytes, a phenomenon termed age-associated thymic involution. Recently, it was reported that age-associated thymic involution did not occur in mice expressing a rearranged transgenic (Tg) TCRalphabeta receptor. This finding implied that an age-associated defect in TCR rearrangement was the major, i...

The segment-polarity class of segmentation genes in Drosophila are primarily involved in the specification of sub-segmental units. In addition, some of the segment-polarity genes have been shown to specify cell fates within the central nervous system. One of these loci, gooseberry, consists of two divergently transcribed genes, gooseberry and gooseberry neuro, which share a paired box as well a...

There are different models that explain growth during development. One model is based on insect and amphibian regeneration studies. This model proposes that growth is directed by pattern, and growth takes place by intercalation at a growth discontinuity; therefore, proliferation should surround the discontinuity. Currently, this model, apart from regenerative studies on mostly adult patterning,...

Repetition avoidance has been intensely studied since Thue’s work in the early 1900’s. In this paper, we consider another type of repetition, called pseudopower, inspired by the Watson-Crick complementarity property of DNA sequences. A DNA single strand can be viewed as a string over the four-letter alphabet {A,C,G, T }, whereinA is the complement of T , while C is the complement of G. Such a D...

Accurate delay models are important for static and dynamic timing analysis of digital circuits, and mandatory for formal verification. However, Függer et al. [IEEE TC 2016] proved that pure and inertial delays, which are employed for dynamic timing analysis in state-of-the-art tools like ModelSim, NC-Sim and VCS, do not yield faithful digital circuit models. Involution delays, which are based o...

We develop a new approach for the computation of Mullineux involution symmetric group and its Hecke algebra using notion crystal isomorphism Iwahori-Matsumoto affine type \(A\). As consequence, we obtain several elementary combinatorial algorithms computation, one which is equivalent to Xu algorithm (and thus original algorithm). simple interpretation these proof that they indeed compute involu...