6,114 research outputs found
Irreducible representations of the symmetric groups from slash homologies of p-complexes
In the 40s, Mayer introduced a construction of (simplicial) -complex by
using the unsigned boundary map and taking coefficients of chains modulo .
We look at such a -complex associated to an -simplex; in which case,
this is also a -complex of representations of the symmetric group of rank
- specifically, of permutation modules associated to two-row compositions.
In this article, we calculate the so-called slash homology - a homology theory
introduced by Khovanov and Qi - of such a -complex. We show that every
non-trivial slash homology group appears as an irreducible representation
associated to two-row partitions, and how this calculation leads to a basis of
these irreducible representations given by the so-called -standard tableaux.Comment: 16 pages, 2 figures. Rewritten the proof of first theorem.
Substantial rearrangement of materials in other sections. Comments welcome
Scott Ranks of Classifications of the Admissibility Equivalence Relation
Let be a recursive language. Let be the set of
-structures with domain . Let be a function with the property that
for all , if and only if
. Then there is some
so that
A Signaling Theory of Grade Inflation
When employers cannot tell whether a school truly has many good students or just gives easy grades, schools have an incentive to inflate grades to help mediocre students, despite concerns about preserving the value of good grades for good students. We construct a signaling model where grades are inflated in equilibrium. The inability to commit to an honest grading policy reduces the informativeness of grades and hurts schools. Grade inflation by one school makes it easier for another school to fool the market with inflated grades. Easy grades are strategic complements, providing a channel to make grade exaggeration contagious.
Suspense
In a dynamic model of sports competition, we show that when spectators care only about the level of effort exerted by contestants, rewarding schemes that depend linearly on the final score difference provide more efficient incentives for efforts than schemes based only on who wins and loses. This result is puzzling because rank order schemes are the dominant forms of reward in sports competitions. The puzzle can be explained if one takes into account the fact that spectators also care about the suspense in the game. We define spectators\\' demand for suspense as greater utility derived from contestants\\' efforts when the game is closer. As the demand for suspense increases, so does the advantage of rank order schemes relative to linear score difference schemes. When the demand for suspense is sufficiently high, the optimal rank order scheme dominates all linear score difference schemes, and with plausible additional restrictions, it dominates a broad class of incentive schemes that reward contestants on the basis of the final score difference.
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