On the irreducibility of a polynomial associated with the Strong Factorial Conjecture
نویسنده
چکیده
The Strong Factorial Conjecture of E. Edo and A. van den Essen [3] is concerned with the linear functional L on the space of complex polynomials defined by sending a monomial generator z1 1 · · · zn n to (a1!) · · · (an!). The conjecture asserts that for a non-zero multi-variable complex polynomial F , the maximum number of consecutive zeroes that may appear in the sequence {L(F ) : n ≥ 1} is N(F ) − 1, where N(F ) is the number of monomials appearing in F with nonzero coefficient. In the second author’s dissertation [12], he considered the irreducibility in Z[x] of the polynomials
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