Jonas Sjöstrand - Academia.edu (original) (raw)
Papers by Jonas Sjöstrand
Dcg, 2005
In the boolean case originally considered by Bier, we show that all the spheres produced by his c... more In the boolean case originally considered by Bier, we show that all the spheres produced by his construction are shellable, which yields "many shellable spheres", most of which lack convex realization. Finally, we present simple explicit formulas for the g-vectors of these simplicial spheres and verify that they satisfy a strong form of the g-conjecture for spheres.
Combinatorics, Probability & Computing, 2003
OSTRAND Abstract. For a random graph on n vertices where the edges appear with individual rates, ... more OSTRAND Abstract. For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning forest. For a random bipartite graph we give a formula for the expected time at which
Operations Research, 2007
In a two-sided version of the famous secretary problem, employers search for a secretary at the s... more In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.
Mathematical Social Sciences, 2006
We consider stable three-dimensional matchings of three genders (3GSM). Alkan [Alkan, A., 1988. N... more We consider stable three-dimensional matchings of three genders (3GSM). Alkan [Alkan, A., 1988. Non-existence of stable threesome matchings. Mathematical Social Sciences 16, 207–209] showed that not all instances of 3GSM allow stable matchings. Boros et al. [Boros, E., Gurvich, V., Jaslar, S., Krasner, D., 2004. Stable matchings in three-sided systems with cyclic preferences. Discrete Mathematics 286, 1–10] showed that if
Advances in Applied Mathematics, 2001
We answer some questions concerning the so-called σ-game of Sutner [Linear cellular automata and ... more We answer some questions concerning the so-called σ-game of Sutner [Linear cellular automata and the Garden of Eden, Math. Intelligencer11 (1989), 49–53]. It is played on a graph where each vertex has a lamp, the light of which is toggled by pressing any vertex with an edge directed to the lamp. For example, we show that every configuration of lamps
Journal of Combinatorial Theory, Series A, 2009
We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplan... more We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w ∈ S n is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups.
We consider stable three-dimensional matchings of three categories of agents, such as women, men ... more We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on this problem. Based on computer experiments, we present a couple of conjectures as well as a few counter-examples to other natural but discarded conjectures. In particular, a circular 3D matching is one where women only care about the man, men only care about the dog, and dogs only care about the woman they are matched with. We conjecture that a stable outcome always exists for any circular 3D matching market, and we prove it for markets with at most four agents of each category.
The Swedish rent control system creates a white market for swapping rental contracts and a black ... more The Swedish rent control system creates a white market for swapping rental contracts and a black market for selling rental contracts. Empirical data suggests that in this black-and-white market some people act according to utility functions that are both discontinuous and locally decreasing in money. We discuss Quinzii's theorem for the nonemptiness of the core of generalized house-swapping games, and show how it can be extended to cover the Swedish game.In a second part, we show how this theorem of Quinzii and her second theorem on nonemptiness of the core in two-sided models are both special cases of a more general theorem.
A fundamental fact in two-sided matching is that if a market allows several stable outcomes, then... more A fundamental fact in two-sided matching is that if a market allows several stable outcomes, then one is optimal for all men in the sense that no man would prefer another stable outcome. We study a related phenomenon of asymmetric equilibria in a dynamic market where agents enter and search for a mate for at most n rounds before exiting again. Assuming independent preferences, we find that this game has multiple equilibria, some of which are highly asymmetric between sexes. We also investigate how the set of equilibria depends on a sex difference in the outside option of not being mated at all.
For a random graph on n vertices where the edges appear with individual rates, we give exact form... more For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning forest.
In a two-sided version of the famous secretary problem, employers search for a secretary at the s... more In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.
Advances in Applied Mathematics, 2012
ABSTRACT We consider a family of birth processes and birth-and-death processes on Young diagrams ... more ABSTRACT We consider a family of birth processes and birth-and-death processes on Young diagrams of integer partitions of n. This family incorporates three famous models from very different fields: Rostʼs totally asymmetric particle model (in discrete time), Simonʼs urban growth model, and Moranʼs infinite alleles model. We study stationary distributions and limit shapes as n tends to infinity, and present a number of results and conjectures.
The Ramanujan Journal, Jan 1, 2010
Bentley et al studied the turnover rate in popularity toplists in a 'random copying' model of cul... more Bentley et al studied the turnover rate in popularity toplists in a 'random copying' model of cultural evolution. Based on simulations of a model with population size N , list length ℓ and invention rate µ, they conjectured a remarkably simple formula for the turnover rate: ℓ √ µ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically. 60G50 · 05A17
Dcg, 2005
In the boolean case originally considered by Bier, we show that all the spheres produced by his c... more In the boolean case originally considered by Bier, we show that all the spheres produced by his construction are shellable, which yields "many shellable spheres", most of which lack convex realization. Finally, we present simple explicit formulas for the g-vectors of these simplicial spheres and verify that they satisfy a strong form of the g-conjecture for spheres.
Combinatorics, Probability & Computing, 2003
OSTRAND Abstract. For a random graph on n vertices where the edges appear with individual rates, ... more OSTRAND Abstract. For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning forest. For a random bipartite graph we give a formula for the expected time at which
Operations Research, 2007
In a two-sided version of the famous secretary problem, employers search for a secretary at the s... more In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.
Mathematical Social Sciences, 2006
We consider stable three-dimensional matchings of three genders (3GSM). Alkan [Alkan, A., 1988. N... more We consider stable three-dimensional matchings of three genders (3GSM). Alkan [Alkan, A., 1988. Non-existence of stable threesome matchings. Mathematical Social Sciences 16, 207–209] showed that not all instances of 3GSM allow stable matchings. Boros et al. [Boros, E., Gurvich, V., Jaslar, S., Krasner, D., 2004. Stable matchings in three-sided systems with cyclic preferences. Discrete Mathematics 286, 1–10] showed that if
Advances in Applied Mathematics, 2001
We answer some questions concerning the so-called σ-game of Sutner [Linear cellular automata and ... more We answer some questions concerning the so-called σ-game of Sutner [Linear cellular automata and the Garden of Eden, Math. Intelligencer11 (1989), 49–53]. It is played on a graph where each vertex has a lamp, the light of which is toggled by pressing any vertex with an edge directed to the lamp. For example, we show that every configuration of lamps
Journal of Combinatorial Theory, Series A, 2009
We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplan... more We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w ∈ S n is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups.
We consider stable three-dimensional matchings of three categories of agents, such as women, men ... more We consider stable three-dimensional matchings of three categories of agents, such as women, men and dogs. This was suggested long ago by Knuth (1976), but very little seems to have been published on this problem. Based on computer experiments, we present a couple of conjectures as well as a few counter-examples to other natural but discarded conjectures. In particular, a circular 3D matching is one where women only care about the man, men only care about the dog, and dogs only care about the woman they are matched with. We conjecture that a stable outcome always exists for any circular 3D matching market, and we prove it for markets with at most four agents of each category.
The Swedish rent control system creates a white market for swapping rental contracts and a black ... more The Swedish rent control system creates a white market for swapping rental contracts and a black market for selling rental contracts. Empirical data suggests that in this black-and-white market some people act according to utility functions that are both discontinuous and locally decreasing in money. We discuss Quinzii's theorem for the nonemptiness of the core of generalized house-swapping games, and show how it can be extended to cover the Swedish game.In a second part, we show how this theorem of Quinzii and her second theorem on nonemptiness of the core in two-sided models are both special cases of a more general theorem.
A fundamental fact in two-sided matching is that if a market allows several stable outcomes, then... more A fundamental fact in two-sided matching is that if a market allows several stable outcomes, then one is optimal for all men in the sense that no man would prefer another stable outcome. We study a related phenomenon of asymmetric equilibria in a dynamic market where agents enter and search for a mate for at most n rounds before exiting again. Assuming independent preferences, we find that this game has multiple equilibria, some of which are highly asymmetric between sexes. We also investigate how the set of equilibria depends on a sex difference in the outside option of not being mated at all.
For a random graph on n vertices where the edges appear with individual rates, we give exact form... more For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning forest.
In a two-sided version of the famous secretary problem, employers search for a secretary at the s... more In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.
Advances in Applied Mathematics, 2012
ABSTRACT We consider a family of birth processes and birth-and-death processes on Young diagrams ... more ABSTRACT We consider a family of birth processes and birth-and-death processes on Young diagrams of integer partitions of n. This family incorporates three famous models from very different fields: Rostʼs totally asymmetric particle model (in discrete time), Simonʼs urban growth model, and Moranʼs infinite alleles model. We study stationary distributions and limit shapes as n tends to infinity, and present a number of results and conjectures.
The Ramanujan Journal, Jan 1, 2010
Bentley et al studied the turnover rate in popularity toplists in a 'random copying' model of cul... more Bentley et al studied the turnover rate in popularity toplists in a 'random copying' model of cultural evolution. Based on simulations of a model with population size N , list length ℓ and invention rate µ, they conjectured a remarkably simple formula for the turnover rate: ℓ √ µ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically. 60G50 · 05A17