Related papers: Lecture notes on the Ein-Popa extension result
We construct unital extensions of the higher order peak algebras defined by Krob and the third author in [Ann. Comb. 9 (2005), 411--430.], and show that they can be obtained as homomorphic images of certain subalgebras of the…
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…
Bessenrodt and Ono's work on additive and multiplicative properties of the partition function and DeSalvo and Pak's paper on the log-concavity of the partition function have generated many beautiful theorems and conjectures. In January…
We discuss and give elementary proofs of results of Brion and of Lawrence-Varchenko on the lattice-point enumerator generating functions for polytopes and cones. This largely expository note contains a new proof of Brion's Formula using…
H. J. Zassenhaus conjectured that any unit of finite order and augmentation one in the integral group ring of a finite group $G$ is conjugate in the rational group algebra to an element of $G$. One way to verify this is showing that such…
Index of notation added. Shortening of some section, simplification of some of the arguments, some small added results and strengthening of thm 3.10. Also a significant re-writing of the last section.
By a celebrated result of Ku\v{c}era and Slaman (DOI:10.1137/S0097539799357441), the Martin-L\"of random left-c.e. reals form the highest left-c.e. Solovay degree. Barmpalias and Lewis-Pye (arXiv:1604.00216) strengthened this result by…
We present an exposition of the theory of finite automata augmented with a multiply-only register storing an element of a given monoid or group. Included are a number of new results of a foundational nature. We illustrate our techniques…
Let H[a_0,n] be the class of functions p(z)=a_0+a_nz^n+... which are analytic in the open unit disk U. For p(z)in H[1,2], M. Nunokawa, S. Owa, N. Uyanik and H. Shiraishi (Math. Comput. Modelling. 55 (2012), 1245-1250) have shown some…
We analyze the causal-observational languages that were introduced in Barbero and Sandu (2018), which allow discussing interventionist counterfactuals and functional dependencies in a unified framework. In particular, we systematically…
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
We extend the well-known Dumont--Thomas numeration systems to $\mathbb{Z}$ using an approach inspired by the two's complement numeration system. Integers in $\mathbb{Z}$ are canonically represented by a finite word (starting with…
The distribution of $\alpha p$ modulo one, where $p$ runs over the rational primes and $\alpha$ is a fixed irrational real, has received a lot of attention. It is natural to ask for which exponents $\nu>0$ one can establish the infinitude…
The Magnus expansion provides an exponential representation of one-parameter operator families, expressed as a series expansion in its generators. This is useful for example in quantum mechanics for expressing a unitary evolution determined…
We give a new proof of the classical result due to Rodney Y. Sharp and Peter Vamos on the dimension of tensor product of a finite number of field extensions of a given field.
The families of right (left) translation finite subsets of a discrete infinite group $\Gamma$ are defined and shown to be ideals. Their kernels $Z_R$ and $Z_L$ are identified as the closure of the set of products $pq$ ($p\cdot q$) in the…
This work, shows how propositional resolution can be generalized to obtain a resolution proof system for constrained pseudo-propositional logic (CPPL), which is an extension resulted from inserting the natural numbers with few constraints…
The paper contains theorems on extending sections of line bundles from divisors to the ambient space, inspired by various results of Siu, Kawamata, and especially Hacon-McKernan and Takayama. Applications are given to basepoint-freeness, to…
We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…
We develop an idea of Evans and O'Connell, Englander and Pinsky and Duquesne and Winkel by giving a pathwise construction of the so called `backbone' decomposition for supercritical superprocesses. Our results also complement a related…