Let B ∈ Z[x] be a polynomial with b = B(0). Let S be a complete residue class modulo b containing 0. We attempt to classify the polynomials B and residue classes S so that for every polynomial P ∈ Z[x] there exists a polynomial Q with coefficients in S such that P ≡ Q (mod B).

1.1 Generalization Quite often, a problem one wants to show NP-Complete (NPC) is a generalization of a known NPC problem. For example, the Traveling Seller problem is a generalization of the Hamiltonian Circuit Problem. Showing that the generalized problem is NPhard is trivial: the identity reduction suffices. Or to put it another way, a polynomial time algorithm for the generalized problem is ...

In this paper the single cycle T-functions are studied. Making use of the explicit formulas of sum and product of 2-adic integers, we present the necessary and sufficient conditions on the generalized polynomial p̃(x) = a0⊕a1x + ⊕ · · · + ⊕adx d(mod2n) being a single cycle T-function. Furthermore, for any given generalized polynomial, we can deduce some expressions about its coefficients by whic...

In this note it is observed that nonvanishing of a generalized LittlewoodRichardson coefficient of any type can be decided in polynomial time assuming the conjecture in [2, 6] that the coefficients of the associated stretching quasi-polynomial are nonnegative.

The deenitions of descent, excedance, major index, inversion index and Denert's statistic for the elements of the symmetric group S d are generalized It is shown, bijectively, that excedances and descents are equidistributed, and the corresponding descent polynomial, analogous to the Eulerian polynomial , is computed as the f {eulerian polynomial of a simple polynomial. The descent polynomial i...

There is a type of distance-regular graph, said to be $Q$-polynomial. In this paper we investigate generalized $Q$-polynomial property involving graph that not necessarily distance-regular. We give detailed description an example associated with the projective geometry $L_N(q)$.