Families of parking functions counted by the schröder and baxter numbers

We define two new families of parking functions: one counted by Schröder numbers and the other by Baxter numbers. These families both include the well-known class of non-decreasing parking functions, which is counted by Catalan numbers and easily represented by Dyck paths, and they both are included in the class of underdiagonal sequences, which are bijective to permutations. We investigate their combinatorial properties exhibiting bijections between these two families and classes of lattice paths (Schröder paths and triples of non-intersecting lattice paths) and discovering a link between them and some classes of pattern avoiding permutations. Then, we provide a quite natural generalization for each of these families that results in some enumeration problems tackled by ECO method

Skin Potential Recordings During Cystometry in Spinal-cord Injured Patients

In order to investigate autonomic mechanisms associated with bladder filling and bladder contraction, skin potentials from the hands and the feet of 32 spinal cord injured patients were recorded during cystometry. All had a complete clinical loss of motor and sensory function below the lesion, but in 3 patients. the autonomic lesion was electrophysiologically assessed as incomplete. In patients with a complete autonomic lesion, any rise in intravesical pressure associated with bladder hyperreflexia induced SP responses below the level of the lesion. SP responses were never obtained during bladder filling, as the intravesical pressure remained low. These results tend to confirm those of Guttmann and Whitteridge, but differ in so far as SP responses at the foot were a regular finding in all paraplegic and in most tetraplegic patients. Furthermore, bladder contraction failed to elicit SP responses below the level of the lesion in patients with an incomplete autonomic lesion. This study emphasises the importance of assessing the integrity of the autonomic nervous pathways when dealing with autonomic mechanisms in spinal cord injured patients. The possible relation between SP responses and bladder neck dysfunction is further discussed