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Combinatorial Games under Auction Play
Abstract A Richman game is a combinatorial game in which, rather than alternating moves, the two players bid for the privilege of making the next move. The theory of such games is a hybrid betweenExpand
Richman games
A Richman game is a combinatorial game in which, rather than alternating moves, the two players bid for the privilege of making the next move. We find optimal strategies for both the case where aExpand
Sets with a negative number of elements
We will define an analog of a set which can contain either a positive or negative number of elements. We will allow sums to be calculated over an arbitrary hybrid set. This will lead us to aExpand
Stable Winning Coalitions
We introduce the notion of a stable winning coalition in a multiplayer game as a new system of classification of games. An axiomatic refinement of this classification for three-player games is alsoExpand
A selected survey of umbral calculus
We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of "magic rules" forExpand
Sequences of Binomial Type with Persistent Roots
Abstract We find all sequences of polynomials (pn)n⩾0with persistent roots (i.e.,pn(x)=cn(x−r1)(x−r2)···(x−rn)) that are of binomial type in Viskov's generalization of Rota's umbral calculus toExpand
Voting Fairly: Transitive Maximal Intersecting Families of Sets
  • D. Loeb, A. Conway
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 July 2000
TLDR
The enumeration of the 207,650,662,008 maximal families of intersecting subsets of X whose group of symmetries is transitive for |X|<13. Expand
A generalization of the binomial coefficients
  • D. Loeb
  • Computer Science, Mathematics
  • Discret. Math.
  • 14 August 1992
TLDR
The question of what is the best generalization of the factorial and the binomial coefficient is posed and several examples, derive their combinatorial properties, and demonstrate their interrelationships are given. Expand
A generalization of the Stirling numbers
  • D. Loeb
  • Computer Science, Mathematics
  • Discret. Math.
  • 28 May 1992
TLDR
The Stirling numbers of the first kind $s(a,k)$ are generalized to the case where $a$ may be an arbitrary real number, and new combinatorial properties held by the classical StirlingNumbers are discovered. Expand
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