17,538 research outputs found
Quivers of monoids with basic algebras
We compute the quiver of any monoid that has a basic algebra over an
algebraically closed field of characteristic zero. More generally, we reduce
the computation of the quiver over a splitting field of a class of monoids that
we term rectangular monoids (in the semigroup theory literature the class is
known as ) to representation theoretic computations for group
algebras of maximal subgroups. Hence in good characteristic for the maximal
subgroups, this gives an essentially complete computation. Since groups are
examples of rectangular monoids, we cannot hope to do better than this.
For the subclass of -trivial monoids, we also provide a semigroup
theoretic description of the projective indecomposables and compute the Cartan
matrix.Comment: Minor corrections and improvements to exposition were made. Some
theorem statements were simplified. Also we made a language change. Several
of our results are more naturally expressed using the language of Karoubi
envelopes and irreducible morphisms. There are no substantial changes in
actual result
Selling Technology: The Changing Shape of Sales in an Information Economy
[Excerpt] This book describes and explains the changing nature of sales through the daily experiences of salespeople, engineers, managers, and purchasing agents who construct markets for emergent technologies through their daily engagement in sales interactions… [It] provides a grounded empirical account of sales work in an area that has been the subject of insufficient study, namely contemporary industrial markets where firms trade with other firms
Anick-type resolutions and consecutive pattern avoidance
For permutations avoiding consecutive patterns from a given set, we present a
combinatorial formula for the multiplicative inverse of the corresponding
exponential generating function. The formula comes from homological algebra
considerations in the same sense as the corresponding inversion formula for
avoiding word patterns comes from the well known Anick's resolution.Comment: 16 pages. Preliminary version, comments are welcom
P versus NP and geometry
I describe three geometric approaches to resolving variants of P v. NP,
present several results that illustrate the role of group actions in complexity
theory, and make a first step towards completely geometric definitions of
complexity classes.Comment: 20 pages, to appear in special issue of J. Symbolic. Comp. dedicated
to MEGA 200
Invariance: a Theoretical Approach for Coding Sets of Words Modulo Literal (Anti)Morphisms
Let be a finite or countable alphabet and let be literal
(anti)morphism onto (by definition, such a correspondence is determinated
by a permutation of the alphabet). This paper deals with sets which are
invariant under (-invariant for short).We establish an
extension of the famous defect theorem. Moreover, we prove that for the
so-called thin -invariant codes, maximality and completeness are two
equivalent notions. We prove that a similar property holds in the framework of
some special families of -invariant codes such as prefix (bifix) codes,
codes with a finite deciphering delay, uniformly synchronized codes and
circular codes. For a special class of involutive antimorphisms, we prove that
any regular -invariant code may be embedded into a complete one.Comment: To appear in Acts of WORDS 201
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