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pro vyhledávání: '"Pang, C. Y."'
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled planar trees extending the Loday-Ronco and Malvenuto-Reutenauer Hopf
Externí odkaz:
http://arxiv.org/abs/2109.05434
Autor:
Pang, C. Y. Amy
We extend an algebra of Mantaci and Reutenauer, acting on the free associative algebra, to a vector space of operators acting on all graded connected Hopf algebras. These operators are convolution products of certain involutions, which we view as hyp
Externí odkaz:
http://arxiv.org/abs/2108.09097
Publikováno v:
Indian Journal of Otolaryngology & Head & Neck Surgery; Oct2024, Vol. 76 Issue 5, p4086-4090, 5p
Autor:
Pang, C. Y. Amy
We develop a general theory for Markov chains whose transition probabilities are the coefficients of descent operators on combinatorial Hopf algebras. These model the breaking-then-recombining of combinational objects. Examples include the various ca
Externí odkaz:
http://arxiv.org/abs/1609.04312
Publikováno v:
Journal of Combinatorial Theory, Series A, 158(2018), 36-65
The number of alternating runs is a natural permutation statistic. We show it can be used to define some commutative subalgebras of the symmetric group algebra, and more precisely of the descent algebra. The Eulerian peak algebras naturally appear as
Externí odkaz:
http://arxiv.org/abs/1609.04393
Autor:
Pang, C. Y. Amy
A function on the state space of a Markov chain is a "lumping" if observing only the function values gives a Markov chain. We give very general conditions for lumpings of a large class of algebraically-defined Markov chains, which include random walk
Externí odkaz:
http://arxiv.org/abs/1508.01570
Autor:
Pang, C. Y. Amy
Recently, Diaconis, Ram and I created Markov chains out of the coproduct-then-product operator on combinatorial Hopf algebras. These chains model the breaking and recombining of combinatorial objects. Our motivating example was the riffle-shuffling o
Externí odkaz:
http://arxiv.org/abs/1503.08368
Autor:
Pang, C. Y. Amy
This thesis introduces a way to build Markov chains out of Hopf algebras. The transition matrix of a "Hopf-power Markov chain" is (the transpose of) the matrix of the coproduct-then-product operator on a combinatorial Hopf algebra with respect to a s
Externí odkaz:
http://arxiv.org/abs/1412.8221
The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" p
Externí odkaz:
http://arxiv.org/abs/1206.3620
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