Non-Commutative Sylvester's Determinantal Identity
نویسندگان
چکیده
منابع مشابه
Non-Commutative Sylvester's Determinantal Identity
Sylvester’s identity is a classical determinantal identity with a straightforward linear algebra proof. We present combinatorial proofs of several non-commutative extensions, and find a β-extension that is both a generalization of Sylvester’s identity and the β-extension of the quantum MacMahon master theorem.
متن کاملNon-commutative Sylvester’s determinantal identity, preprint
Sylvester's identity is a classical determinantal identity with a straightforward linear algebra proof. We present a new, combinatorial proof of the identity, prove several non-commutative versions, and find a β-extension that is both a generalization of Sylvester's identity and the β-extension of the MacMahon master theorem.
متن کاملNon-commutative extensions of classical determinantal identities
We present several non-commutative extensions of MacMahon Master Theorem and Sylvester’s Identity. The proofs are combinatorial and new even in the classical (commutative) cases. Résumé. Nous présentons plusieurs extensions noncommutatives du Master théorème de MacMahon et de l’identité de Sylvester. Même dans les cas classiques (commutatifs), les démonstrations sont nouvelles et de nature comb...
متن کاملNon-commutative computations: lower bounds and polynomial identity testing
In the setting of non-commutative arithmetic computations, we define a class of circuits that generalize algebraic branching programs (ABP). This model is called unambiguous because it captures the polynomials in which all monomials are computed in a similar way (that is, all the parse trees are isomorphic). We show that unambiguous circuits of polynomial size can compute polynomials that requi...
متن کاملDirected Graphs of Commutative Rings with Identity
The directed graph of a ring is a graphical representation of its additive and multiplicative structure. Using the directed edge relationship (a, b) → (a + b, a · b), one can create a directed graph for every ring. This paper focuses on the structure of the sources in directed graphs of commutative rings with identity, with special concentration in the finite and reduced cases. Acknowledgements...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2007
ISSN: 1077-8926
DOI: 10.37236/960