Let p be an odd prime and let n be a natural number. In this article we determine the irreducible constituents of the permutation module induced by the action of the symmetric group Sn on the cosets of a Sylow p-subgroup Pn. As a consequence, we determine the number of irreducible representations of the corresponding Hecke algebra H(Sn, Pn, 1P n).

Let p⩾5 be a prime and let n be a natural number. In this article, we describe the irreducible constituents of the induced characters ϕ↑frakturSn for arbitrary linear characters ϕ of a Sylow p‐subgroup Pn of the symmetric group Sn, generalising results of Giannelli and Law (J. Algebra 506 (2018) 409–428). By doing this, we introduce Sylow branching coefficients for symmetric groups.

A 73-year-old man presented to the emergency department with lethargy and influenza-like symptoms. Incidentally, prominent blue sclera and blue-grey skin discolouration to the periorbital skin, pinnae, neck, upper and lower limbs, hands, feet, fingernails and toenails were noted. His general practitioner (GP) had previously ceased amiodarone, believing it to be the causative agent. A literature search confirms the side effects were likely due to minocycline, which the patient had been taking for 10 years. Long-term minocycline use is associated with scleral and skin hyperpigmentation, with no apparent adverse effect on ocular structure or function. The pigmentation may reverse with cessation of minocycline, or it may be permanent. Amiodarone may also cause skin hyperpigmentation, but scleral pigmentation is not a known association. This case report explores the side effect profiles of these two drugs, and highlights the potential for confusion regarding causative agents when used concurrently.

Let p be a prime number. In this article we study the restriction to Sn−1 of irreducible characters of degree coprime to p of Sn. In particular, we study the combinatorial properties of the subgraph Y p ′ of the Young graph Y. This is an extension to odd primes of the work done in [1] for p = 2.

The deep inferior epigastric perforator (DIEP) flap is the gold standard in post-mastectomy breast reconstruction. Improved patient outcomes, reduced operating time and reduced complication rates are reportedly observed over consecutive DIEP series within surgical centres. The aim of this study is to investigate whether outcomes following DIEP flap reconstruction improve over time, by assessing two patient cohorts undergoing the procedure at a microsurgical unit seven years apart. A case analysis was undertaken to identify all patients who underwent primary DIEP flap reconstruction in 2011 and 2018. Outcomes recorded included clinic appointments, operating time, number of primary operations, additional operations and procedures, along with co-morbidities, BMI and radiotherapy rates. Immediate versus delayed and unilateral versus bilateral breast reconstruction was also recorded. Seven patients underwent primary DIEP reconstruction in 2011 and 29 in 2018. There was a significant reduction in additional operations performed in 2018 (p-value = 0.007) and a significant reduction in number of procedures (p-value = 0.043). When adjusted for an outlier, the total operating time for unilateral DIEP reconstruction was significantly shorter in 2018 (p-value = 0.018), along with reduced primary and total operating time for 2018 bilateral reconstructions. The 2018 cohort also had lower complication rates and fewer clinic appointments. This study illustrates how outcomes can improve with experience of DIEP flap reconstruction. The more complex DIEP flap requires investment in terms of skill acquisition and operative time, but is balanced by improvement in patient outcomes.