It is shown that $A:=H_{1,\eta}(G)$, the Sympectic Reflection Algebra, has $T_G$ independent traces, where number of conjugacy classes elements without eigenvalue 1 belonging to finite group $G$ generated by system symplectic reflections. Simultaneously, we show algebra $A$, considered as a superalgebra with natural parity, $S_G$ supertraces, -1 $G$. We consider also $A$ Lie $A^L$ and $A^S$. if...

We study the problems of bounding number weak and strong independent sets in r-uniform, d-regular, n-vertex linear hypergraphs with no cross-edges. In case sets, we provide an upper bound that is tight up to first order term for all (fixed) r≥3, d n going infinity. r=3, second term, improving on a result Ordentlich–Roth (2004). The tightness set established by explicit construction 3-uniform, c...